Gumbeldf

Purpose

Gumbel distribution.

Synopsis

prob = gumbeldf(function,x,a,b)

Description

Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Gumbel distribution. This distribution is also known as the Type I extreme value distribution. It is an alternative to the Weibull distribution.

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 (-inf,inf).
• 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 = mode/location parameter (real).
• b = scale parameter (real and positive).

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.

Examples

Cumulative:

>> prob = gumbeldf('c',0.99,0.5,1) prob =

   0.5419

>> x = [0:0.1:10]; >> plot(x,gumbeldf('c',x,2),'b-',x,gumbeldf('c',x,0.5),'r-')

Density:

>> prob = gumbeldf('d',0.99,0.5,1) prob = 0.3320 >> x = [0:0.1:10]; >> plot(x,gumbeldf('d',x,2),'b-',x,gumbeldf('d',x,0.5),'r-')

Quantile:

>> prob = gumbeldf('q',0.99,0.5,1) prob =

   5.1001

Random:

>> prob = gumbeldf('r',[4 1],2,1) ans =

   3.8437
   2.6508
   2.3566
   4.2479

See Also

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