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

$f(x)={\frac {1}{2b}}\exp \left(-{\frac {|x-a|}{b}}\right)$

$F(x)={\frac {1}{2}}\exp \left[-{\frac {a-x}{b}}\right]\mathrm {I} \left(x<a\right)+1-{\frac {1}{2}}\exp \left[-{\frac {x-a}{b}}\right]\mathrm {I} \left(x\geq a\right)$

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

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