PLS_Toolbox Documentation: betadf	< ttest2u	cauchydf >

betadf

Purpose

Beta distribution.

Synopsis

prob = betadf(function,x,a,b,options)

Description

Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Beta distribution.           

This distribution is commonly used to model activity time. In its usual form, the data must be in (0,1), but this toolbox will allow both a location and scale parameter (in addition to the a and b above). This may be symmetric or asymmetric.

INPUTS:

          function =   [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].

                         x =   matrix in which the sample data is stored, in the interval (0,1).

                                 for function=quantile - matrix with values in the interval (0,1).

                                 for function=random - vector indicating the size of the random matrix to create.

                         a =   scale parameter (real and nonnegative).

                         b =   shape parameter (real and nonnegative).

Note: If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.

Note: Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results.

Options

options is a structure array with the following fields:

                     name:   'options', name indicating that this is an options structure,

                   scale:   {1}, scale for the ordinate, and

                 offset:   {0}, offset for the ordinate.

The default options structure can be retrieved using: options = betadf('options').

Examples

Cumulative:

>> prob = betadf('c', [0.85 0.9],1,2)

prob =

0.9775                0.9900

>> x    = [0:0.01:1];

>> plot(x,betadf('c',x,1,2),'b-',x,betadf('c',x,0.5,0.5),'r-')

Density:

>> prob = betadf('d', 0.9, 1, 2)

prob =

0.2000

>> x    = [0:0.01:1];

>> plot(x,betadf('d',x,1,2),'b-',x,betadf('d',x,0.5,0.5),'r-')

Quantile:

>> prob = betadf('q',[0.9775 0.9900]',1,2)

prob =

    0.8500

    0.9000

Random:

>> prob = betadf('r',[5 1],1,2)

prob =

    0.3791

    0.2549

    0.8169

    0.0216

    0.1516

See Also

cauchydf, chidf, expdf, gammadf, gumbeldf, laplacedf, lognormdf, logisdf, normdf, paretodf, raydf, triangledf, unifdf, weibulldf