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

See Also

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