A Study on Transformation of Self-similar Processes with Arbitrary Marginal Distributions

Abstract

AbstractStochastic discrete-event simulation studies of communication networks often require a mechanism to transform self-similar processes with normal marginal distributions into self-similar processes with arbitrary marginal distributions. The problem of generating a self-similar process of a given marginal distribution and an autocorrelation structure is difficult and has not been fully solved. Our results presented in this paper provide clear experimental evidence that the autocorrelation function of the input process is not preserved in the output process generated by the inverse cumulative distribution function (ICDF) transformation, where the output process has an infinite variance. On the other hand, it preserves autocorrelation functions of the input process where the output marginal distributions (exponential, gamma, Pareto with α= 20.0, uniform and Weibull) have finite variances, and the ICDF transformation is applied to long-range dependent self-similar processes with normal marginal distributions.KeywordsSelf-similar processArbitrary marginal distributionAutocorrelation functionInverse cumulative distribution functionStochastic simulation