{ Analytica Model Laplacian_distributi, encoding="UTF-8" }
SoftwareVersion 5.2.9
LinkModule Laplacian_distributi
Title: Laplacian distribution library
Description: In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together back-to-back, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.~
~
Credit: The above description is quoted from wikipedia's entry on the Laplacian distribution.
Author: Dale Rice~
Lumina Decision Systems
Date: Mon, Jan 6, 2020 12:29 PM
NodeSize: 56,32
WindState: 2,559,325,720,350
FontStyle: Arial,15
FileInfo: 0,LinkModule Laplacian_distributi,2,2,0,0,Laplacian distribution library.ana
Function Laplacian(mean,scale ; ~
over : optional named;~
singleSampleMethod : optional hidden scalar~
)
Title: Laplacian
Description: The Laplacian distribution.
Definition: Local u := Uniform(0,1,over: ...over, singleSampleMethod:singleSampleMethod);~
CumLaplacianInv( u, mean, scale )
NodeLocation: 96,48,1
NodeSize: 48,24
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Function CumLaplacian(x,mean,scale)
Title: CumLaplacian
Description: The cumulative density function for the Laplacian distribution.
Definition: if x>=mean then 0.5 + CumExponential( x-mean, 1/scale )/2~
else 0.5 - CumExponential( mean-x, 1/ scale ) / 2
NodeLocation: 232,48,1
NodeSize: 64,24
WindState: 2,586,320,720,350
Function CumLaplacianInv(p,mean,scale)
Title: CumLaplacianInv
Description: The inverse cumulative density function (aka quantile function) for the Laplacian distribution.
Definition: Local tmp := CumExponentialInv( 2*abs(p-0.5), 1/scale ) ;~
if p>=0.5 then mean + tmp else mean - tmp
NodeLocation: 400,48,1
NodeSize: 80,24
WindState: 2,586,320,720,350
Function DensLaplacian(x,mean,scale)
Title: DensLaplacian
Description: The density function for the Laplacian distribution.
Definition: 0.5 * DensExponential( abs(x-mean), 1/scale )
NodeLocation: 568,48,1
NodeSize: 80,24
WindState: 2,586,320,720,350
Close Laplacian_distributi