Generating matrix exponential random variates

In this paper we present a technique for generating random variates from an empirical distribution using the matrix exponential representation of the distribution. In our experience, a matrix exponential representation of an empirical distribution produces random variates with an excellent fit with the empirical distribution. This technique is particularly important when the empirical data is very bursty, i.e., has a high variance. In this paper we discuss how to find the matrix exponential representation of an empirical distribution and we present our technique for generating random variates from the empirical distribution using its matrix exponential representation. We show how the matrix exponential representation of an empirical distribution is found through an example and then we show that matrix exponential random variates are an excellent fit with the empirical data through an chi(2) goodness-of-fit test.