laplacedf Documentation


PLS_Toolbox Documentation: laplacedf	< gumbeldf	logisdf >

laplacedf

Purpose

Laplace distribution.

Synopsis

prob = laplacedf(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 Laplace distribution.

This distribution is a symmetric distribution also known as the double exponential distribution. It is more peaked than the normal distribution Leptokurtic rather than mesokurtic means that it has a sharper peak at the mean in the density plot than a similar normal density

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 positive).

b = shape 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 = laplacedf('c',0.99,1,2)

prob =

0.4975

>> x = [0:0.1:10];

>> plot(x,laplacedf('c',x,1,2),'b-',x,laplacedf('c',x,3,7),'r-')

Density:

>> prob = laplacedf('d',0.99,1,1)

prob =

0.4950

>> x = [0:0.1:10];

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

Quantile:

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

prob =

4.4120

Random:

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

ans =

0.4549

0.4638

0.3426

0.5011