Abstract

The importance of phase type distribution in modeling activities cannot be under emphasized when both the first and second moments of a distribution are available or when the sequence of data points for computing moments is the information available. In continuous time process, phase type distribution can be viewed to be the distribution of the time to absorption for an absorbing finite state Markov chain, and it is widely used in queueing theories and other fields of applied probabilities with the used of generalized Erlang, Coxian, Hypo-exponential, and Hyper-exponential distributions In this study, fitting analysis of general phase type distribution have been looked into, in order to provide meaningful study into the probability function, mean, kth moment, variance, Laplace Stieltjes transform and squared coefficient of variation of phase type distribution. We begin from the tractability and memory less properties of exponential distribution, and since these properties are not enough, we looked into the passage through a phases of exponential stages by the use of matrix and vector operations to arrive at performance measures. Illustrative examples are demonstrated for various cases to arrive at various values for probability functions, Laplace Stieltjes transform, squared coefficient of variation,kth moment, mean and variance for the phase type distribution.