 |
Download a pdf copy of this help file here |
|
Download a pdf copy of this help file here |
Format: VoseLaplace(m, s, U)
If X and Y are two identical independent Expon(s) distributions, and if X is shifted m to the right of Y, then (X-Y) is a Laplace(m, s) distribution. The Laplace distribution has an unusual, symmetric shape with a sharp peak and tails that are longer than the tails of a Normal distribution. The figure below plots a Laplace(0,1) against a Normal(0,1) distribution:
The Laplace has found a variety of very specific uses, but they nearly all relate to the fact that it has long tails compared to the Normal distribution. It has recently become quite popular in modeling financial variables (Brownian Laplace motion) like stock returns because of the greater tails. The Laplace distribution is very extensively reviewed in the monograph Kotz et al (2001).
When m = 0, and s = 1 we have the standard form of the Laplace distribution, which is also occasionally called 'Poisson's first law of error'. The Laplace distribution is also known as the Double-Exponential distribution (though the Gumbel Extreme Value distribution also takes this name), the Two-Tailed Exponential and the Bilateral Exponential distribution.
Skewness = 0, kurtosis = 6.
VoseLaplace generates values from this distribution or calculates a percentile
VoseLaplaceObject constructs a distribution object for this distribution
VoseLaplaceProb returns the probability density or cumulative distribution function for this distribution
VoseLaplaceProb10 returns the log10 of the probability density or cumulative distribution function
VoseLaplaceFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution
VoseLaplaceFitObject constructs a distribution object of this distribution fitted to data
VoseLaplaceFitP returns the parameters of this distribution fitted to data
