Mathematica Software for the Numerical Generation of Given Distribution with Exponential Autocorrelation Function

This directory includes Mathematica files for generation of samples of a random processes with a given probability density function (PDF) and with an exponential autocorrelation function (ACF). These files also provide a statistical validation of the resulting processes.

The generation method is based on creation of an appropriate stochastic differential equation (SDE) of the first order and solving it by implicit Milstein methods.

The following files are included:

• ProcessWithExpACF.nb and ProcessWithExpACF.m: Mathematica module for random process generation.
• Laplase_Dist_Example.nb: Module applied for generation of Laplace distribution.
• Chi-Square.nb, HalfNormal_Dist.nb, Laplase_Dist_Example_with_Validation.nb: The generation module is applied for χ2, half-normal and Laplase distributions together with validation of code results.
• Laplase_Dist_nomod.nb: The process generation is performed inside the same file without module applied.

Notes:

1. The length of generated sequence influences the validation results. For the best visual results the number of samples, length>= 5*10^6. The main drawback is that takes time...
2. χ2 and half-normal distributions are defined only for positive values, i.e. f(x)=0 for x<0. Moreover, a half-normal distribution has a discontinuity in the orign.

This source code was created and verified with version 11 of Mathematica.