In /usr/share/local/matlab42/toolbox/stats

Contents.m

Statistics Toolbox.
Version 1.0, 15-Sept.-1993
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.6 Date: 1993/09/09 21:49:18
Statistical Plots.

anova1.m

ANOVA1 One-way analysis of variance (ANOVA).
ANOVA1 performs a one-way ANOVA for comparing the means of two or more
groups of data. It returns the p-value for the null hypothesis that the
means of the groups are equal.

P = ANOVA1(X) for matrix, X, treats each column as a separate group,
and determines whether the population means of the columns are equal.
This one-input form of ANOVA1 is appropriate when each group has the
same number of elements (balanced ANOVA).

P = ANOVA1(X,GROUP) has vector inputs X and GROUP. The vector, GROUP,
identifies the group of the corresponding element of X. This two-input
form of ANOVA1 has no restrictions on the number of elements in each
group.

ANOVA1 prints the standard one-way ANOVA table in Figure 1 and displays
a boxplot in Figure2.

Reference: Robert V. Hogg, and Johannes Ledolter, Engineering Statistics
Macmillan 1987 pp. 205-206.

Copyright(c) 1993 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/08/18 20:13:41

anova2.m

ANOVA2 Two-way analysis of variance.
ANOVA2(X,REPS) performs a balanced two-way ANOVA for comparing the
means of two or more columns and two or more rows of the sample in X.
The data in different columns represent changes in one factor. The data
in different rows represent changes in the other factor. If there is
more than one observation per row-column pair, then the argument, REPS,
indicates the number of observations per "cell". A cell contains REPS
number of rows.

For example, if REPS = 3, then each cell contains 3 rows and the total
number of rows must be a multiple of 3. If X has 12 rows, and REPS = 3,
then the "row" factor has 4 levels (3*4 = 12). The second level of the
row factor goes from rows 4 to 6.

Reference: Robert V. Hogg, and Johannes Ledolter, Engineering Statistics
Macmillan 1987 pp. 227-231.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/08/26 18:16:22

betacdf.m

BETACDF Beta cumulative distribution function.
P = BETACDF(X,A,B) returns the beta cumulative distribution
function with parameters A and B at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

BETAINC does the computational work.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.5.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:16

betainv.m

BETAINV Inverse of the beta cumulative distribution function (cdf).
X = BETAINV(P,A,B) returns the inverse of the beta cdf with
parameters A and B at the values in P.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

BETAINV uses Newton's method to converge to the solution.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964.

B.A. Jones 1-12-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:18

betapdf.m

BETAPDF Beta probability density function.
Y = BETAPDF(X,A,B) returns the beta probability density
function with parameters A and B at the values in X.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.33.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:21

betarnd.m

BETARND Random matrices from beta distribution.
R = BETARND(A,B) returns a matrix of random numbers chosen
from the beta distribution with parameters A and B.
The size of R is the common size of A and B if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. Alternatively, R = BETARND(A,B,M,N) returns an M by N matrix.

Reference:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:23

betastat.m

BETASTAT Mean and variance for the beta distribution.
[MN,VAR] = BETASTAT(A,B) returns the mean and variance
of the beta distribution with parameters A and B.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.33.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:25

BINOCDF.M

BINOCDF Binomial cumulative distribution function.
Y=BINOCDF(X,N,P) returns the binomial cumulative distribution
function with parameters N and P at the values in X.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

The algorithm uses the cumulative sums of the binomial masses.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.20.

B.A. Jones 1-12-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:29

binoniv.m

BINOINV Inverse of the binomial cumulative distribution function (cdf).
X = BINOINV(Y,N,P) returns the inverse of the binomial cdf with
parameters N and P. Since the binomial distribution is
discrete, BINOINV returns the least integer X such that
the binomial cdf evaluated at X, equals or exceeds Y.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Note that X takes the values 0,1,2,...,N.

B.A. Jones 1-12-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:31

binopdf.m

BINOPDF Binomial probability density function.
Y = BINOPDF(X,N,P) returns the binomial probability density
function with parameters N and P at the values in X.
Note that the density function is zero unless X is an integer.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.20.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:34

binornd.m

BINORND Random matrices from a binomial distribution.
R = BINORND(N,P,MM,NN) is an MM-by-NN matrix of random
numbers chosen from a binomial distribution with parameters N and P.

The size of R is the common size of N and P if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter.
Alternatively, R = BINORND(N,P,MM,NN) returns an MM by NN matrix.

The method is direct using the definition of the binomial
distribution as a sum of Bernoulli random variables.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986
See Lemma 4.1 on page 428, method on page 524.

B.A. Jones 1-12-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:37

binostat.m

BINOSTAT Mean and variance of the binomial distribution.
Y = BINOSTAT(N,P) returns the mean and variance of the
binomial distibution with parameters N and P.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.20.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:39

boxplot.m

BOXPLOT Display boxplots of a data sample.
BOXPLOT(X,NOTCH,SYM,VERT,WHIS) produces a box and whisker plot for
each column of X. The box has lines at the lower quartile, median,
and upper quartile values. The whiskers are lines extending from
each end of the box to show the extent of the rest of the data.
Outliers are data with values beyond the ends of the whiskers.

NOTCH = 1 produces a notched-box plot. Notches represent a robust
estimate of the uncertainty about the means for box to box comparison.
NOTCH = 0 (default) produces a rectangular box plot.
SYM sets the symbol for the outlier values if any (default='+').
VERT = 0 makes the boxes horizontal (default: VERT = 1, for vertical).
WHIS defines the length of the whiskers as a function of the IQR
(default = 1.5). If WHIS = 0 then BOXPLOT displays all data
values outside the box using the plotting symbol, SYM.

BOXPLOT calls BOXUTIL to do the actual plotting.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/26 18:33:17

boxutil.m

BOXUTIL Produces a single box plot.
BOXUTIL(X) is a utility function for BOXPLOT, which calls
BOXUTIL once for each column of its first argument. Use
BOXPLOT rather than BOXUTIL.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:44

cdf.m

CDF Computes a chosen cumulative distribution function.
P = CDF(NAME,X,A) returns the named cumulative distribution
function, which uses parameter A, at the the values in X.
P = CDF(NAME,X,A,B) returns the named cumulative distribution
function, which uses parameters a and b, at the the values in X.
Similarly for P = CDF(NAME,X,A,B,C).

The name can be: 'beta' or 'Beta', 'bino' or 'Binomial',
'chi2' or 'Chisquare','exp' or 'Exponential', 'f' or 'F',
'gam' or 'Gamma','geo' or 'Geometric','hyge' or 'Hypergeometric',
'norm' or 'Normal','poiss' or 'Poisson','t' or 'T','unif' or 'Uniform',
'unid' or 'Discrete Uniform','weib' or 'Weibull'.

CDF calls many specialized routines that do the calculations.

D. Zwillinger 3-91, B. Jones 10-92
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/25 14:27:54

chi2cdf.m

CHI2CDF Chi-square cumulative distribution function.
P = CHI2CDF(X,V) returns the chi-square cumulative distribution
function with V degrees of freedom at the values in X.
The chi-square density function with V degrees of freedom,
is the same as a gamma density function with parameters V/2 and 2.

The size of P is the common size of X and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.4.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:49

chi2inv.m

CHI2INV Inverse of the chi-square cumulative distribution function (cdf).
X = CHI2INV(P,V) returns the inverse of the chi-square cdf with V
degrees of freedom at the values in P. The chi-square cdf with V
degrees of freedom, is the gamma cdf with parameters V/2 and 2.

The size of X is the common size of P and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.4.
[2] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, 1970, section 10.2 (page 144)

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:51

chi2pdf.m

CHI2PDF Chi-square probability density function (pdf).
Y = CHI2PDF(X,V) returns the chi-square pdf with V degrees
of freedom at the values in X. The chi-square pdf with V
degrees of freedom, is the gamma pdf with parameters V/2 and 2.

The size of Y is the common size of X and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986, pages 402-403.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:55

chi2rnd.m

CHI2RND Random matrices from chi-square distribution.
R = CHI2RND(V) returns a matrix of random numbers chosen
from the chi-square distribution with V degrees of freedom.
The size of R is the size of V.
Alternatively, R = CHI2RND(V,M,N) returns an M by N matrix.

CHI2RND calls GAMRND since the chi-square distribution
is a special case of the gamma distribution. (See Devroye, page 403)

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:53:57

chi2stat.m

CHI2STAT Mean and variance for the chi-square distribution.
[MN,VAR] = CHI2STAT(V) returns the mean and variance
of the chi-square distribution with V degrees of freedom.

A chi-square random variable, with V degrees of freedom,
is identical to a gamma random variable with parameters V/2 and 2.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986, pages 402-403.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:00

distchck.m

DISTCHCK Checks the argument list for the probability functions.

B.A. Jones 1-22-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:03

disttool.m

DISTTOOL Demonstration of many probability distributions.
DISTTOOL creates interactive plots of probability distributions.
This is a demo that displays a plot of the cdf or pdf of
the distributions in the Statistics Toolbox.

Use popup menus to change the distibution (Normal to Binomial) or
the function (cdf to pdf).

You can change the parameters of the distribution by typing
a new value or by moving a slider.

You can interactively calculate new values by dragging a reference
line across the plot.

Call DISTTOOL without arguments.

B.A. Jones 3-15-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.11 Date: 1993/09/28 15:59:18

expcdf.m

EXPCDF Exponential cumulative distribution function.
P = EXPCDF(X,LAMBDA) returns the exponential cumulative
distribution function with parameter LAMBDA at the values in X.

The size of P is the common size of X and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.28.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:10

expinv.m

EXPINV Inverse of the exponential cumulative distribution function.
X = EXPINV(P,LAMBDA) returns the inverse of the exponential
cumulative distribution function, with parameter LAMBDA,
at the values in P.

The size of X is the common size of P and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:12

exppdf.m

EXPPDF Exponential probability density function.
Y = EXPPDF(X,LAMBDA) returns the exponential probability density
function with parameter LAMBDA at the values in X.

The size of Y is the common size of X and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.28.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:14

exprnd.m

EXPRND Random matrices from exponential distribution.
R = EXPRND(LAMBDA) returns a matrix of random numbers chosen
from the exponential distribution with parameter LAMBDA.
The size of R is the size of LAMBDA.
Alternatively, R = EXPRND(LAMBDA,M,N) returns an M by N matrix.

EXPRND uses a simple inversion method. See Devroye, page 392.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:18

expstat.m

EXPSTAT Mean and variance of the exponential distribution.
[MN,VAR] = EXPSTAT(LAMBDA) returns the mean and variance
of the exponential distribution with parameter LAMBDA.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.28.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:21

fcdf.m

FCDF F cumulative distribution function.
P = FCDF(X,V1,V2) returns the F cumulative distribution function
with V1 and V2 degrees of freedom at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.6.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:24

finv.m

FINV Inverse of the F cumulative distribution function.
X=FINV(P,V1,V2) returns the inverse of the F distribution
function with V1 and V2 degrees of freedom, at the values in Y.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.6.2

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:27

fpdf.m

FPDF F probability density function.
Y = FPDF(X,V1,V2) returns the F distribution probability density
function with V1 and V2 degrees of freedom at the values in X.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

References:
[1] J. K. Patel, C. H. Kapadia, and D. B. Owen, "Handbook
of Statistical Distributions", Marcel-Dekker, 1976.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:29

frnd.m

FRND Random matrices from the F distribution.
R = FRND(V1,V2) returns a matrix of random numbers chosen
from the F distribution with parameters V1 and V2.
The size of R is the common size of V1 and V2 if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. Alternatively, R = FRND(V1,V2,M,N) returns an M by N matrix.

FRND calls BETARND.
See Devroye, Theorem 4.1 on page 430, case D.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:32

fstat.m

FSTAT Mean and variance for the F distribution.
[MN,VAR] = FSTAT(V1,V2) returns the mean (MN) and variance (VAR)
of the F distribution with V1 and V2 degrees of freedom.
Note that the mean of the F distribution is undefined if V1
is less than 3. The variance is undefined for V2 less than 5.

References:
[1] W. H. Beyer, "CRC Standard Probability and Statistics",
CRC Press, Boston, 1991, page 23.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:35

fsurfht.m

FSURFHT Interactive contour plot of a function.
FSURFHT(FUN,XLIM,YLIM) is an interactive contour plot of the function
specified by the text variable FUN. The x-axis limits are specified
by XLIMS = [XMIN XMAX] and the y-axis limits specified by YLIMS.
FSURFHT(FUN,XLIM,YLIM,P1,P2,P3,P4,P5) allows for five optional parameters
that you can supply to the function FUN. The first two arguments of FUN
are the x-axis variable and y-axis variable, respectively.

There are vertical and horizontal reference lines on the plot whose
intersection defines the current x-value and y-value. You can drag
these dotted white reference lines and watch the calculated z-values (at
the top of the plot) update simultaneously. Alternatively, you can get a
specific z-value by typing the x-value and y-value into editable text
fields on the x-axis and y-axis respectively.

B.A. Jones 5-23-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.9 Date: 1993/09/28 16:06:47

gamcdf.m

GAMCDF Gamma cumulative distribution function.
P = GAMCDF(X,A,B) returns the gamma cumulative distribution
function with parameters A and B at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Some references refer to the gamma distribution with a single
parameter. This corresponds to the default of B = 1.

GAMMAINC does computational work.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986. p. 401.
[2] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.32.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:38

gaminv.m

GAMINV Inverse of the gamma cumulative distribution function (cdf).
X = GAMINV(P,A,B) returns the inverse of the gamma cdf with
parameters A and B, at the probabilities in P.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

GAMINV uses Newton's method to converge to the solution.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 6.5.

B.A. Jones 1-12-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:41

gampdf.m

GAMPDF Gamma probability density function.
Y = GAMPDF(X,A,B) returns the gamma probability density function
with parameters A and B, at the values in X.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Some references refer to the gamma distribution with a single
parameter. This corresponds to the default of B = 1.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986, pages 401-402.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/09/10 22:00:05

gamrnd.m

GAMRND Random matrices from gamma distribution.
R = GAMRND(A,B) returns a matrix of random numbers chosen
from the gamma distribution with parameters A and B.
The size of R is the common size of A and B if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. Alternatively, R = GAMRND(A,B,M,N) returns an M by N matrix.

Some references refer to the gamma distribution
with a single parameter. This corresponds to GAMRND
with B = 1. (See Devroye, pages 401-402.)

GAMRND uses a rejection or an inversion method depending on the
value of A.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

B.A. Jones 2-1-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/09/24 20:05:40

gamstat.m

GAMSTAT Mean and variance for the gamma distribution.
[MN,VAR] = GAMSTAT(A,B) returns the mean and variance
of the gamma distribution with parameters A and B. By default,
B = 1.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986, page 7.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:48

gas.mat

geocdf.m

GEOCDF Geometric cumulative distribution function.
Y=GEOCDF(X,P) returns the geometric cumulative distribution
function with probability, P, at the values in X.

The size of Y is the common size of X and P. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.24.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:51

geoinv.m

GEOINV Inverse of the geometric cumulative distribution function.
X = GEOINV(Y,P) returns the inverse of the geometric cdf with
parameter P. Since the geometric distribution is discrete,
GEOINV returns the smallest integer X, such that the value of the
cdf at X, equals or exceeds Y.

The size of X is the common size of Y and P. A scalar input
functions as a constant matrix of the same size as the other input.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:53

geomean.m

GEOMEAN Geometric mean.
M = GEOMEAN(X) returns the geometric mean of the input.
When X is a vector with n elements, GEOMEAN(X) returns of the
the n-th root of the product of the elements.
For a matrix input, GEOMMEAN(X) returns a row vector containing
the geometric mean of each column of X.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:54:55

geopdf.m

GEOPDF Geometric probability density function (pdf).
Y = GEOPDF(X,P) returns the geometric pdf with probability, P,
at the values in X.

The size of Y is the common size of X and P. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.24.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/26 18:43:05

geornd.m

GEORND Random matrices from geometric distribution.
R = GEORND(P) returns a matrix of random numbers chosen from a
geometric distribution where the parameter, P, is the probability
of success in any trial.

The size of R is the size of P. Alternatively,
R = GEORND(P,M,N) returns an M by N matrix.

The method is direct. (Devroye, page 87)

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:00

geostat.m

GEOSTAT Mean and variance of the geometric distribution.
[MN,VAR] = GEOSTAT(P) returns the mean and variance
of the geometric distribution with parameter P.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.24.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:03

harmmean.m

HARMMEAN Harmonic mean.
M = HARMMEAN(X) returns the harmonic mean of the data.
The harmonic mean is the inverse of the mean of the inverses
of the elements.
For matrix X, HARMMEAN(X) returns a row vector containing
the harmonic mean of each column of X.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:06

hogg.mat

hygecdf.m

HYGECDF Hypergeometric cumulative distribution function.
P = HYGECDF(X,M,K,N) returns the hypergeometric cumulative
distribution function with parameters M, K, and N
at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

B.A. Jones 2-23-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:11

hygeinv.m

HYGEINV Inverse of the hypergeometric cumulative distribution function (cdf).
X = HYGEINV(P,M,K,N) returns the inverse of the hypergeometric
cdf with parameters M, K, and N. Since the hypergeometric
distribution is discrete, HYGEINV returns the smallest integer X,
such that the hypergeometric cdf evaluated at X, equals or exceeds P.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:14

hygepdf.m

HYGEPDF Hypergeometric probability density function.
Y = HYGEPDF(X,M,K,N) returns the hypergeometric probability
density function at X with integer parameters M, K, and N.
Note: The density function is zero unless X is an integer.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Reference:
[1] Mood, Alexander M., Graybill, Franklin A. and Boes, Duane C.,
"Introduction to the Theory of Statistics, Third Edition", McGraw Hill
1974 p. 91.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:16

hygernd.m

HYGERND Random matrices from a hypergeometric distribution.
R = HYGERND(M,K,N) returns a matrix of random numbers chosen from
a hypergeometric distribution with parameters M, K, and N.
The size of R is the common size of M, K, and N. Alternatively,
R = HYGERND(M,K,N,MM,NN) returns an MM by NN matrix.

HYGERND uses an inversion method.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:19

hygestat.m

HYGESTAT Mean and variance for the hypergeometric distribution.
[MN,VAR] = HYGESTAT(M,K,N) returns the mean and variance
of the hypergeometric distribution with parameters M, K, and N.

Reference:
[1] Mood, Alexander M., Graybill, Franklin A. and Boes, Duane C.,
"Introduction to the Theory of Statistics, Third Edition", McGraw Hill
1974 p. 538.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:21

A NAME="icdf">icdf.m

ICDF Computes a chosen inverse cumulative distribution function.
X = ICDF(NAME,P,A) returns the named inverse cumulative distribution
function, which uses parameter A, at the the values in X.
X = ICDF(NAME,P,A,B) returns the named cumulative distribution
function, which uses parameters A and B, at the the values in X.
Similarly for X = ICDF(NAME,P,A,B,C).

The name can be: 'beta' or 'Beta', 'bino' or 'Binomial',
'chi2' or 'Chisquare','exp' or 'Exponential', 'f' or 'F',
'gam' or 'Gamma','geo' or 'Geometric','hyge' or 'Hypergeometric',
'norm' or 'Normal','poiss' or 'Poisson','t' or 'T','unif' or 'Uniform',
'unid' or 'Discrete Uniform','weib' or 'Weibull'.

ICDF calls many specialized routines that do the calculations.

D. Zwillinger 3-91, B. Jones 10-92
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/25 14:32:47

igr.m

IQR Interquartile Range.
Y = IQR(X) calculates the interquarile range (IQR) of the input.
Given a vector input, the IQR is formed by subtracting the 25th
percentile of the data from the 75th percentile of the data.
(See PRCTILE)

The IQR is a robust estimate of the spread of the data since changes
in the upper and lower 25 of the data do not affect it.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:25

mad.m

MAD Mean absolute deviation.
Y = MAD(X) calculates the mean absolute deviation (MAD) of X.
For matrix X, MAD returns a row vector containing the MAD of each
column.

The algorithm involves subtracting the mean of X from X,
taking absolute values, and then finding the mean of the result.

References:
[1] L. Sachs, "Applied Statistics: A Handbook of Techniques",
Springer-Verlag, 1984, page 253.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:28

mileage.mat

moore.mat

normcdf.m

NORMCDF Normal cumulative distribution function (cdf).
P = NORMCDF(X,MU,SIGMA) computes the normal cdf with mean MU and
standard deviation SIGMA at the values in X.

The size of P is the common size of X, MU and SIGMA. A scalar input
functions as a constant matrix of the same size as the other inputs.

Default values for MU and SIGMA are 0 and 1 respectively.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.2.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:31

norminv.m

NORMINV Inverse of the normal cumulative distribution function (cdf).
X = NORMINV(P,MU,SIGMA) finds the inverse of the normal cdf with
mean, MU, and standard deviation, SIGMA.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Default values for MU and SIGMA are 0 and 1 respectively.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 7.1.1 and 26.2.2

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:33

normpdf.m

NORMPDF Normal probability density function (pdf).
Y = NORMPDF(X,MU,SIGMA) Returns the normal pdf with mean, MU,
and standard deviation, SIGMA, at the values in X.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Default values for MU and SIGMA are 0 and 1 respectively.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.26.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:36

normplot.m

NORMPLOT Displays a normal probability plot.
H = NORMPLOT(X) makes a normal probability plot of the
data in X. For matrix, X, NORMPLOT displays a plot for each column.
H is a handle to the plotted lines.

The purpose of a normal probability plot is to graphically assess
whether the data in X could come from a normal distribution. If the
data are normal the plot will be linear. Other distribution types
will introduce curvature in the plot.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/10/01 14:21:23

normrnd.m

NORMRND Random matrices from normal distribution.
R = NORMRND(MU,SIGMA) returns a matrix of random numbers chosen
from the normal distribution with parameters MU and SIGMA.

The size of R is the common size of MU and SIGMA if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. Alternatively, R = NORMRND(MU,SIGMA,M,N) returns an M by N
matrix.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:41

normstat.m

NORMSTAT Mean and variance for the normal distribution.
[MN,VAR] = NORMSTAT(MU,SIGMA) returns the mean and variance of
the normal distribution with parameters MU and SIGMA.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.26.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:44

pdf.m

PDF Computes a chosen probability density function.
Y = PDF(NAME,X,A) returns the named probability density
function, which uses parameter A, at the the values in X.
Y = PDF(NAME,X,A,B,) returns the named probability density
function, which uses parameters A and B, at the the values in X.
Similarly for Y = PDF(NAME,X,A,B,C).

The name can be: 'beta' or 'Beta', 'bino' or 'Binomial',
'chi2' or 'Chisquare','exp' or 'Exponential', 'f' or 'F',
'gam' or 'Gamma','geo' or 'Geometric','hyge' or 'Hypergeometric',
'norm' or 'Normal','poiss' or 'Poisson','t' or 'T','unif' or 'Uniform',
'unid' or 'Discrete Uniform','weib' or 'Weibull'.

PDF calls many specialized routines that do the calculations.

D. Zwillinger 5-91, B. Jones 10-92
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/25 14:30:11

poisscdf.m

POISSCDF Poisson cumulative distribution function.
P = POISSCDF(X,LAMBDA) computes the Poisson cumulative
distribution function with parameter LAMBDA at the values in X.

The size of P is the common size of X and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.22.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:50

poissinv.m

POISSINV Inverse of the Poisson cumulative distribution function (cdf).
X = POISSINV(P,LAMBDA) returns the inverse of the Poisson cdf
with parameter lambda. Since the Poisson distribution is discrete,
POISSINV returns the smallest value of X, such that the poisson
cdf evaluated, at X, equals or exceeds P.

The size of X is the common size of P and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

B.A. Jones 1-15-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:53

poisspdf.m

POISSPDF Poisson probability density function.
Y = POISSPDF(X,LAMBDA) returns the Poisson probability density
function with parameter LAMBDA at the values in X.

The size of Y is the common size of X and LAMBDA. A scalar input
functions as a constant matrix of the same size as the other input.

Note that the density function is zero unless X is an integer.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.22.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:56

poissrnd.m

POISSRND Random matrices from Poisson distribution.
R = POISSRND(LAMBDA) returns a matrix of random numbers chosen
from the Poisson distribution with parameter LAMBDA.

The size of R is the size of LAMBDA. Alternatively,
R = POISSRND(A,B,M,N) returns an M by N matrix.

POISSRND uses a waiting time method.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986 page 504.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:55:58

poisstat.m

POISSTAT Mean and variance for the Poisson distribution.
[MN,VAR] = POISSTAT(LAMBDA) returns the mean and variance of
the Poisson distribution with parameter LAMBDA.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.22.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:01

polyconf.m

POLYCONF Polynomial evaluation and confidence interval estimation.
If p is a vector of length n+1 whose elements are the coefficients
of a polynomial, then y = POLYCONF(p,x) is the value of the
polynomial evaluated at x.
y = p(1)*x^n + p(2)*x^(n-1) + ... + p(n)*x + p(n+1)
If X is a matrix or vector, the polynomial is evaluated at all
points in X.

[y,delta] = POLYCONF(p,x,S,alpha) uses the optional output, S,
generated by POLYFIT to generate confidence intervals,
Y +/- DELTA.If the errors in the data input to POLYFIT are
independent normal with constant variance, Y +/- DELTA contains
100(1-ALPHA) of future predictions. The default value of ALPHA is
0.05, which corresponds to 95 confidence intervals.

5-11-93 B.A. Jones
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/06/24 14:40:02

polydata.mat

polytool.m

POLYTOOL Fits a polynomial to (x,y) data and displays an interactive graph.
POLYTOOL(X,Y,N,ALPHA) is a prediction plot that provides a Nth degree
polynomial curve fit to (x,y) data. It plots a 100(1 - ALPHA) percent
global confidence interval for predictions as two red curves. The
default value for N is 1 and the default value for ALPHA is 0.05,
which produces a linear model and 95 confidence intervals respectively.

You can drag the dotted white witness line and watch the predicted
values update simultaneously. Alternatively, you can get a specific
prediction by typing the "X" value into an editable text field.
A pop-up menu at the top allows you to change the degree of the
polynomial fit.

B.A. Jones 3-15-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.7 Date: 1993/09/28 16:08:44

popcorn.mat

prctile.m

PRCTILE gives the percentiles of the sample in X.
Y = PRCTILE(X,P) returns a value that is greater than P percent
of the values in X. For example, if P = 50 Y is the median of X.

P may be either a scalar or a vector. For scalar P, Y is a row
vector containing Pth percentile of each column of X. For vector P,
the ith row of Y is the P(i) percentile of each column of X.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:10

qqplot.m

QQPLOT Displays an empirical quantile-quantile plot.
QQPLOT(X,Y) makes an empirical QQ-plot of the quantiles of
the data set X versus the quantiles of the data set Y.
H = QQPLOT(X,Y,PVEC) allows you to specify the plotted quantiles in
the vector PVEC. H is a handle to the plotted lines.

The default quantiles are those of the smaller data set.

The purpose of the quantile-quantile plot is to determine whether
the samples in X and Y come from the same distribution type (parameter
values may be different.) If the samples do come from the same
distribution, the plot will be linear.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:13

random.m RANDOM Generates random numbers from a named distribution.
R = RANDOM(NAME,A,M,N) returns an M-by-N array of random
numbers from the named distribution with parameter A.
R = RANDOM(NAME,A,B,M,N) returns an M-by-N array of random
numbers from the named distribution with parameters A, and B.
R = RANDOM(NAME,A,B,C,M,N) returns an M-by-N array of random
numbers from the named distribution with parameters A, B, and C.

The name can be: 'beta' or 'Beta', 'bino' or 'Binomial',
'chi2' or 'Chisquare','exp' or 'Exponential', 'f' or 'F',
'gam' or 'Gamma','geo' or 'Geometric','hyge' or 'Hypergeometric',
'norm' or 'Normal','poiss' or 'Poisson','t' or 'T','unif' or 'Uniform',
'unid' or 'Discrete Uniform','weib' or 'Weibull'.

The default value for both M and N is 1.

RANDOM calls many specialized routines that do the calculations.

D. Zwillinger 5-91, B. Jones 10-92
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/25 14:33:52

randtool.m RANDTOOL Demonstration of many random number generators.
RANDTOOL(ACTION) creates a histogram of random samples from many
distributions. This is a demo that displays a histograms of random
samples from the distributions in the Statistics Toolbox.

Change the parameters of the distribution by typing in a new
value or by moving a slider.

Output the current sample to the variable ans by pressing
the output button.

Change the sample size by typing any positive integer in the
sample size edit box.

Change the distribution type using the popup menu.
r = RANDTOOL('output') returns the current sample in r.

B.A. Jones 3-22-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.11 Date: 1993/09/28 16:01:40

range.m

RANGE The range is the difference between the maximum and minimum values.
Y = RANGE(X) calculates the range of the input.
For matrices RANGE(X) is a vector containing the range for each column.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:19

regress.m

REGRESS Performs multiple linear regression using least squares.
b = REGRESS(y,X) returns the vector of regression coefficients, B.
Given the linear model: y = Xb,
(X is an nxp matrix, y is the nx1 vector of observations.)
[B,BINT,R,RINT,STATS] = REGRESS(y,X,alpha) uses the input, ALPHA
to calculate 100(1 - ALPHA) confidence intervals for B and the
residual vector, R, in BINT and RINT respectively.
The vector STATS contains the R-square statistic along with the F
and p values for the regression.

References:
[1] Samprit Chatterjee and Ali S. Hadi, "Influential Observations,
High Leverage Points, and Outliers in Linear Regression",
Statistical Science 1986 Vol. 1 No. 3 pp. 379-416.
[2] N. Draper and H. Smith, "Applied Regression Analysis, Second
Edition", Wiley, 1981.

B.A. Jones 3-04-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.4 Date: 1993/10/04 12:26:29

rndcheck.m

RNDCHECK error checks the argument list for the random number generators.

B.A. Jones 1-22-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:24

statdemo.m STATDEMO Demonstrate some of the capabilities of the Statistics Toolbox.
STATDEMO displays a set of buttons for choosing a specific demo.

Copyright (c) 1984-93 by The MathWorks, Inc.
Revision: 1.3 Date: 1993/10/04 11:56:23

surfht.m SURFHT Interactive contour plot.
SURFHT(Z) is an interactive contour plot of the matrix Z treating the
values in Z as height above the plane. The x-values are the column
indices of Z while the y-values are the row indices of Z.
SURFHT(x,y,Z), where x and y are vectors specify the x and y-axes on the
contour plot. The length of x and y must match the number of rows in Z.

There are vertical and horizontal reference lines on the plot whose
intersection defines the current x-value and y-value. You can drag
these dotted white reference lines and watch the interpolated z-values
(at the top of the plot) update simultaneously. Alternatively, you can
get a specific interpolated z-value by typing the x-value and y-value
into editable text fields on the x-axis and y-axis respectively.

B.A. Jones 5-23-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.8 Date: 1993/09/28 16:04:12

tcdf.m

TCDF Student's T cumulative distribution function (cdf).
P = TCDF(X,V) computes the cdf for Student's T distribution
with V degrees of freedom, at the values in X.

The size of P is the common size of X and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.7.
[2] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986
[3] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, 1970, Section 10.3, pages 144-146.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:26

tinv.m

TINV Inverse of Student's T cumulative distribution function (cdf).
X=TINV(P,V) returns the inverse of Student's T cdf with V degrees
of freedom, at the values in P.

The size of X is the common size of P and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.6.2

B.A. Jones 1-18-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:29

tpdf.m

TPDF Probability density function (pdf) for Student's T distribution
Y = TPDF(X,V) returns the pdf of Student's T distribution with
V degrees of freedom, at the values in X.

The size of Y is the common size of X and V. A scalar input
functions as a constant matrix of the same size as the other input.

References:
[1] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, New York, 1970, Section 10.3, pages 144-146.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:31

trimmean.m

TRIMMEAN The trimmed mean of X is a robust estimate of the sample location.
M = TRIMMEAN(X,PERCENT) calculates the mean of X excluding the highest
and lowest percent/2 of the data. For matrices, TRIMMEAN(X) is a vector
containing the trimmed mean for each column. The scalar, PERCENT,
must take values between 0 and 100.

For matrix, X, M = TRIMMEAN(X,PERCENT) is a row vector containing the
trimmed mean for each column of X.

B.A. Jones 3-04-93
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:34

trnd.m

TRND Random matrices from Student's T distribution.
R = TRND(V) returns a matrix of random numbers chosen
from the T distribution with V degrees of freedom.
The size of R is the size of V.
Alternatively, R = TRND(V,M,N) returns an M by N matrix.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:36

tstat.m

TSTAT Mean and variance for the student's t distribution.
[MN,VAR] = TSTAT(V) returns the mean and variance of
Student's T distribution with V degrees of freedom.

References:
[1] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, New York, 1970, Section 10.3, pages 144-146.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:40

ttest.m

TTEST Hypothesis test: Compares the sample average to a constant.
[H,SIG] = TTEST(X,M,ALPHA,TAIL) performs a T-test to determine
if a sample from a normal distribution (in X) could have mean M.
M = 0, ALPHA = 0.05 and TAIL = 0 by default.

The Null hypothesis is: "mean is equal to M".
For TAIL=0, alternative: "mean is not M".
For TAIL=1, alternative: "mean is greater than M"
For TAIL=-1, alternative: "mean is less than M"
TAIL = 0 by default.

ALPHA is desired significance level.
SIG is the probability of observing the given result by chance
given that the null hypothesis is true. Small values of SIG cast
doubt on the validity of the null hypothesis.
H=0 => "Do not reject null hypothesis at significance level of alpha."
H=1 => "Reject null hypothesis at significance level of alpha."

References:
[1] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, 1970, page 206.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:43

ttest2.m

TTEST2 Hypothesis test: Compares the averages of two samples.
[H,SIGNIFICANCE CI] = TTEST(X,Y,ALPHA,TAIL) performs a T-test to
determine whether two samples from a normal distribution
(with unknown but equal variances) could have the same mean.

The null hypothesis is: "means are equal".
For TAIL = 0 the alternative hypothesis is: "means are not equal."
For TAIL = 1, alternative: "mean of X is greater than mean of Y."
For TAIL = -1, alternative: "mean of X is less than mean of Y."
TAIL = 0 by default.

ALPHA is desired significance level (ALPHA = 0.05 by default).
SIGNIFICANCE is the probability of observing the given result by
chance given that the null hypothesis is true. Small values of
SIGNIFICANCE cast doubt on the validity of the null hypothesis.
H=0 => "Do not reject null hypothesis at significance level of alpha."
H=1 => "Reject null hypothesis at significance level of alpha."

References:
[1] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, 1970, section 13.4. (Table 13.4.1 on page 210)

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:46

unicdf.m UNIDCDF Uniform (discrete) cumulative distribution function.
P = UNIDCDF(X,N) returns the cumulative distribution function
for a random variable uniform on (1,2,...,N), at the values in X.

The size of P is the common size of X and N. A scalar input
functions as a constant matrix of the same size as the other input.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:49

unidinv.m

UNIDINV Inverse of uniform (discrete) distribution function.
X = UNIDINV(P,N) returns the inverse of the uniform
(discrete) distribution function at the values in P.
X takes the values (1,2,...,N).

The size of X is the common size of P and N. A scalar input
functions as a constant matrix of the same size as the other input.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:51

unipdf.m

UNIDPDF Uniform (discrete) probability density function (pdf).
Y = UNIDPDF(X,N) returns the (discrete) uniform probability
density function on (1,2,...,N) at the values in X.

The size of Y is the common size of X and N. A scalar input
functions as a constant matrix of the same size as the other input.

Y is zero (or NaN) unless X is an integer between 1 and N.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:54

unidrnd.m UNIDRND Random matrices from the discrete uniform distribution.
R = UNIDRND(N) returns a matrix of random numbers chosen
uniformly from the set {1, 2, 3, ... ,N}.

The size of R is the size of N. Alternatively,
R = UNIDRND(N,MM,NN) returns an MM by NN matrix.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:56

unidstat.m

UNIDSTAT Mean and variance for uniform (discrete) distribution.
[MN,VAR] = UNIDSTAT(N) returns the mean and variance of
the (discrete) uniform distribution on {1,2,...,N}

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:56:59

unifcdf.m

UNIFCDF Uniform (continuous) cumulative distribution function (cdf).
P = UNIFCDF(X,A,B) returns the cdf for the uniform distribution
on the interval [A,B] at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

By default, A = 0 and B = 1.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:01

unifinv.m

UNIFINV Inverse of uniform (continuous) distribution function.
X = UNIFINV(P,A,B) returns the inverse of the uniform
(continuous) distribution funcion on the interval [A,B],
at the values in P. By default A = 0 and B = 1.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:04

unifpdf.m

UNIFPDF Uniform (continuous) probability density function (pdf).
Y = UNIFPDF(X,A,B) returns the continuous uniform pdf on the
interval [A,B] at the values in X. By default A = 0 and B = 1.

The size of Y is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.34.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:07

unifrnd.m

UNIFRND Random matrices from continuous uniform distribution.
R = UNIFRND(A,B) returns a matrix of random numbers chosen
from the continous uniform distribution on the interval from A to B.
The size of R is the common size of A and B if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. Alternatively, R = UNIFRND(A,B,M,N) returns an M by N matrix.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/26 19:01:43

unifstat.m

UNIFSTAT Mean and variance of the continuous uniform distribution.
[MN,VAR] = UNIFSTAT(A,B) returns the mean and variance of
the uniform distribution on the interval [A,B].

Reference:
[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical
Functions", Government Printing Office, 1964, 26.1.34.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:12

var.m

VAR Variance.
For vectors, VAR(x) returns the sample variance.
For matrices, VAR(X)is a row vector containing the sample
variance of each column. The variance is the square of the
standard deviation (STD). See also COV.

B.A. Jones 9-30-92
Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/08/26 19:04:29

weibinv.m

WEIBINV Inverse of the Weibull cumulative distribution function (cdf).
X = WEIBINV(P,A,B) returns the inverse of the Weibull cdf with
parameters A and B, at the values in P.

The size of X is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

References:
[1] J. K. Patel, C. H. Kapadia, and D. B. Owen, "Handbook
of Statistical Distributions", Marcel-Dekker, 1976.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:19

weibcdf.m

WEIBCDF Weibull cumulative distribution function (cdf).
P = WEIBCDF(X,A,B) returns the Weibull cdf with parameters A and B
at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Some references refer to the Weibull distribution with a
single parameter. This corresponds to WEIBCDF with A = 1.

References:
[1] J. K. Patel, C. H. Kapadia, and D. B. Owen, "Handbook
of Statistical Distributions", Marcel-Dekker, 1976.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:17

weibdf.m

WEIBPDF Weibull probability density function (pdf).
Y = WEIBPDF(X,A,B) returns the Weibull pdf with parameters
A and B at the values in X.

The size of P is the common size of the input arguments. A scalar input
functions as a constant matrix of the same size as the other inputs.

Some references refer to the Weibull distribution with
a single parameter, this corresponds to WEIBPDF with A = 1.

References:
[1] J. K. Patel, C. H. Kapadia, and D. B. Owen, "Handbook
of Statistical Distributions", Marcel-Dekker, 1976.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.2 Date: 1993/09/22 16:22:59

weibrnd.m

WEIBRND Random matrices from the Weibull distribution.
R = WEIBRND(A,B) returns a matrix of random numbers chosen
from the Weibull distribution with parameters A and B.

The size of R is the common size of A and B if both are matrices.
If either parameter is a scalar, the size of R is the size of the other
parameter. R = WEIBRND(A,B,M,N) returns an M by N matrix.

When A == B, WEIBRND calls EXPRND.
When A ~= B, WEIBRND uses an inversion method.

References:
[1] L. Devroye, "Non-Uniform Random Variate Generation",
Springer-Verlag, 1986

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:24

weibstat.m

WEIBSTAT Mean and variance for Weibull distribution.
[MN,VAR] = WEIBSTAT(A,B) returns the mean and variance of
the Weibull distribution with parameters A and B.

Some references refer to the Weibull distribution with
a single parameter, this corresponds to WEIBSTAT with A = 1.

References:
[1] J. K. Patel, C. H. Kapadia, and D. B. Owen, "Handbook
of Statistical Distributions", Marcel-Dekker, 1976.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:27

ztest.m

ZTEST Hypothesis test: Compares the sample average to a constant.
[H,SIG] = ZTEST(X,M,SIGMA,ALPHA,TAIL) performs a Z-test to determine
whether a sample from a normal distribution (in X) could have mean M
when the standard deviation, SIGMA, is known.
ALPHA = 0.05 and TAIL = 0 by default.

Null hypothesis is: "mean is equal to M".
For TAIL = 0, alternative: "mean is not M".
For TAIL = 1, alternative: "mean is greater than M."
For TAIL = -1, alternative: "mean is less than M."

ALPHA is desired significance level.
SIG is the probability of observing the given result by chance
given that the null hypothesis is true. Small values of SIG cast
doubt on the validity of the null hypothesis.

H=0 => "Do not reject null hypothesis at significance level of alpha."
H=1 => "Reject null hypothesis at significance level of alpha."

References:
[1] E. Kreyszig, "Introductory Mathematical Statistics",
John Wiley, 1970, page 206.

Copyright (c) 1993 by The MathWorks, Inc.
Revision: 1.1 Date: 1993/05/24 18:57:29

Compiled by Jerod M. Parker(jparker@bass.gmu.edu)

June 1994