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# Contents

## PURPOSE

Module WSTATS in WAFO Toolbox.

## SYNOPSIS

This is a script file.

## DESCRIPTION

Module WSTATS in WAFO Toolbox.
Version 2.1.1  07-Sep-2005

What's new
Readme     - New features, bug fixes, and changes in WSTATS.

Parameter estimation
loglike    - Log-likelihood function
wbetafit   - Parameter estimates for Beta data
wchi2fit   - Parameter estimates for Chi squared data
wexpfit    - Parameter estimates for Exponential data
wgamfit    - Parameter estimates for Gamma data
wgamafit   - Is an internal routine for wgamfit
wgevfit    - Parameter estimates for GEV data
wgevlike   - Is an internal routine for wgevfit
wggamfit   - Parameter estimates for Generalized Gamma data
wggambfit  - Is an internal routine for wggamfit
wgpdfit    - Parameter estimates for GPD data
wgpdfit_ml - Internal routine for wgpdfit (ML estimates for GPD data)
wgumbfit   - Parameter estimates for Gumbel data
wgumbafit  - Is an internal routine for wgumbfit
winvgfit   - Parameter estimates for Inverse Gaussian data
wlognfit   - Parameter estimates for Lognormal data
wnormfit   - Parameter estimates for Normal data
wraylfit   - Parameter estimates for Rayleigh data
wtraylfit  - Parameter estimates for Truncated Rayleigh data
wtfit      - Parameter estimates for Student's T data
wweibfit   - Parameter estimates for Weibull data
wweibcfit  - Is an internal routine for wweibfit
wtweibfit  - Parameter estimates for Truncated Weibull data
wtweibfun  - Is an internal routine for wtweibfit
weib2dfit  - Parameter estimates for 2D Weibull data
weib2dlike - 2D Weibull log-likelihood function
dist2dfit  - Parameter estimates for DIST2D data
dist2dsmfun  - Smooths the conditional DIST2D distribution parameters
dist2dsmfun2 - Smooths the conditional DIST2D distribution parameters
mdist2dfit   - Parameter estimates for MDIST2D data
mdist2dlike  - MDIST log-likelihood function

Probability density functions (pdf)
wbetapdf   - Beta probability density function
wchi2pdf   - Chi squared probability density function
wexppdf    - Exponential probability density function
wfpdf      - Snedecor's F probability density function
wfrechpdf  - Frechet probability density function
wgampdf    - Gamma probability density function
wggampdf   - Generalized Gamma probability density function
wgevpdf    - Generalized Extreme Value probability density function
wgpdpdf    - Generalized Pareto probability density function
wgumbpdf   - Gumbel probability density function
winvgpdf   - Inverse Gaussian probability density function
wlognpdf   - Lognormal probability density function
wnormpdf   - Normal probability density function
mvnormpdf  - Multivariate Normal probability density function
wraylpdf   - Rayleigh probability density function
wtraylpdf  - Truncated Rayleigh probability density function
wtpdf      - Student's T probability density function
wweibpdf   - Weibull probability density function
wtweibpdf  - Truncated Weibull probability density function
weib2dpdf  - 2D Weibull probability density function (pdf)
weib2dpdf2 - Joint 2D Weibull probability density function
dist2dpdf  - Joint 2D PDF computed as f(x1|X2=x2)*f(x2)
dist2dpdf2 - Joint 2D PDF computed as f(x1|X2=x2)*f(x2)
mdist2dpdf - Joint 2D PDF due to Plackett given as  f{x1}*f{x2}*G(x1,x2;Psi)
mdist2dpdf2 - Joint 2D PDF due to Plackett given as  f{x1}*f{x2}*G(x1,x2;Psi)

Cumulative distribution functions (cdf)
wbetacdf   - Beta cumulative distribution function
wchi2cdf   - Chi squared cumulative distribution function
wexpcdf    - Exponential cumulative distribution function
wfcdf      - Snedecor's F cumulative distribution function
wfrechcdf  - Frechet cumulative distribution function
wgamcdf    - Gamma cumulative distribution function
wggamcdf   - Generalized Gamma cumulative distribution function
wgevcdf    - Generalized Extreme Value cumulative distribution function
wgpdcdf    - Generalized Pareto cumulative distribution function
wgumbcdf   - Gumbel cumulative distribution function
winvgcdf   - Inverse Gaussian cumulative distribution function
wlogncdf   - Lognormal cumulative distribution function
wnormcdf   - Normal cumulative distribution function
wraylcdf   - Rayleigh cumulative distribution function
wtraylcdf  - Truncated Rayleigh cumulative distribution function
wtcdf      - Student's T  cumulative distribution function
wweibcdf   - Weibull cumulative distribution function
wtweibcdf  - Truncated Weibull cumulative distribution function
weib2dcdf  - Joint 2D Weibull cumulative distribution function
weib2dprb  - Returns the probability for rectangular regions.
dist2dcdf  - Joint 2D CDF computed as int F(X1<v|X2=x2).*f(x2)dx2
dist2dfun  - Is an internal function to dist2dcdf dist2dprb.
dist2dprb  - Returns the probability for rectangular regions.
mdist2dcdf - Joint 2D CDF due to Plackett

Inverse cumulative distribution functions
wbetainv   - Inverse of the Beta distribution function
wchi2inv   - Inverse of the Chi squared distribution function
wexpinv    - Inverse of the Exponential distribution function
wfinv      - Inverse of the Snedecor's F distribution function
wgaminv    - Inverse of the Gamma distribution function
wggaminv   - Inverse of the Generalized Gamma distribution function
wgevinv    - Inverse of the Generalized Extreme Value distribution function
wgpdinv    - Inverse of the Generalized Pareto distribution function
wgumbinv   - Inverse of the Gumbel distribution function
winvginv   - Inverse of the Inverse Gaussian distribution function
wlogninv   - Inverse of the Lognormal distribution function
wnorminv   - Inverse of the Normal distribution function
wraylinv   - Inverse of the Rayleigh distribution function
wtinv      - Inverse of the Student's T distribution function
wweibinv   - Inverse of the Weibull distribution function
weib2dcinv - Inverse of the conditional 2D weibull cdf of X2 given X1.
mdist2dcinv - Inverse of the conditional cdf of X2 given X1.

Random number generators
walpharnd  - Random matrices from a symmetric alpha-stable distribution
wbetarnd   - Random matrices from an Beta distribution
wchi2rnd   - Random matrices from a Chi squared distribution
wexprnd    - Random matrices from an Exponential distribution
wfrnd      - Random matrices from a Snedecor's F distribution
wfrechinv  - Inverse of the Frechet distribution function
wgamrnd    - Random matrices from a Gamma distribution
wggamrnd   - Random matrices from a Generalized Gamma distribution
wgevrnd    - Random matrices from a Generalized Extreme-Value distribution
wgpdrnd    - Random matrices from a Generalized Pareto Distribution
wgumbrnd   - Random matrices from a Gumbel distribution
winvgrnd   - Random matrices from an Inverse Gaussian distribution
wlognrnd   - Random matrices from a Lognormal distribution
wmnormrnd  - Random vectors from a multivariate Normal distribution
wnormrnd   - Random matrices from a Normal distribution
wraylrnd   - Random matrices from a Rayleigh distribution
wtrnd      - Random matrices from a Student's T distribution
wweibrnd   - Random matrices from a Weibull distribution
weib2drnd  - Random numbers from the 2D Weibull distribution.
dist2drnd  - Random points from a bivariate DIST2D distribution
mdist2drnd - Random points from a bivariate MDIST2D distribution

Statistics
wbetastat  - Mean and variance for the Beta distribution.
wchi2stat  - Mean and variance for the Chi squared distribution
wexpstat   - Mean and variance for the Exponential distribution
wfstat     - Mean and variance for the Snedecor's F distribution
wfrechstat - Mean and variance for the Frechet distribution
wgamstat   - Mean and variance for the Gamma distribution
wggamstat  - Mean and variance for the Generalized Gamma distribution
wgevstat   - Mean and variance for the GEV distribution
wgpdstat   - Mean and variance for the Generalized Pareto distribution
wgumbstat  - Mean and variance for the Gumbel distribution
winvgstat  - Mean and variance for the Inverse Gaussian distribution
wlognstat  - Mean and variance for the Lognormal distribution
wnormstat  - Mean and variance for the Normal distribution
wraylstat  - Mean and variance for the Rayleigh
wtstat     - Mean and variance for the Student's T  distribution
wweibstat  - Mean and variance for the Weibull distribution
weib2dstat - Mean and variance for the 2D Weibull distribution
dist2dstat - Mean and variance for the DIST2D distribution
mdist2dstat - Mean and variance for the MDIST2D distribution

Descriptive Statistics
mean       - Computes sample mean (in matlab toolbox)
median     - Computes sample median value (in matlab toolbox)
std        - Computes standard deviation (in matlab toolbox)
var        - Computes sample variance (in matlab toolbox)
cov        - Computes sample covariance matrix (in matlab toolbox)
corrcoef   - Computes sample correlation coefficients (in matlab toolbox)
wkurtosis  - Computes sample kurtosis
wskewness  - Computes sample skewness
iqr        - Computes the Inter Quartile Range
range      - Calculates the difference between maximum and minimum values

Statistical plotting
wgumbplot  - Plots data on a Gumbel distribution paper
wnormplot  - Plots data on a Normal distribution paper
wweibplot  - Plots data on a Weibull distribution paper
wexpplot   - Plots data on a Exponential distribution paper
wraylplot  - Plots data on a Rayleigh distribution paper
wqqplot    - Plots empirical quantile vs empirical quantile
distplot   - Displays a 1D distribution probability plot
empdistr   - Computes and plots the empirical CDF
cempdistr  - Computes and plots the conditional empirical CDF
whisto     - Plots a histogram
kdeplot    - Computes and plots a kernel estimate of PDF
identify   - Identify points on a plot by clicking with the mouse.
pairs      - Pairwise scatter plots.
weib2dcdfplot   - Plot conditional empirical CDF of X1 given X2=x2
weib2dstatplot  - Computes and plots the conditional mean and standard deviation
dist2dcdfplot   - Plot conditional empirical CDF of X1 given X2=x2
dist2dparamplot - Plot parameters of the conditional distribution
dist2dstatplot  - Computes and plots the conditional mean and standard deviation
mdist2dcdfplot  - Plot conditional empirical CDF of X1 given X2=x2
mdist2dstatplot - Computes and plots the conditional mean and standard deviation

Hypothesis Tests
wgumbtest  - Tests whether the shape parameter in a GEV is equal to zero

Design of Experiments
yates      - Calculates main and interaction effects using Yates' algorithm.
ryates     - Reverse Yates' algorithm to give estimated responses
fitmodel   - Fits response by polynomial
alias      - Alias structure of a fractional design
cdr        - Complete Defining Relation
cl2cnr     - Column Label to Column Number
cnr2cl     - Column Number to Column Label
ffd        - Two-level Fractional Factorial Design
getmodel   - Return the model parameters
sudg       - Some Useful Design Generators
cplot      - Cubic plot of responses
nplot      - Normal probability plot of effects

Misc
comnsize   - Check if all input arguments are either scalar or of common size.

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

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