Discrete Erlang Mixed Distributions and their Properties
Beatrice M. Gathongo *
Department of Mathematics, University of Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
The proposed research is on discrete Erlang mixtures. Properties of the mixed distributions analyzed include raw and central moments, which have been derived in terms of moments of the mixing distributions. Cumulants obtained from the cumulant generating functions were also used in deriving the moments. The posterior distribution and posterior moments are also among properties presented. Bayesian, moments and maximum likelihood methods have been applied in parameter estimation. Additionally, the mixture distributions have been fitted to two data sets to test their goodness of fit. Some methods and special functions used in the study are the exponential series, logarithmic series, geometric series, modified Bessel function of the first kind, and the Touchard polynomials. The discrete mixing distributions used are the geometric, Poisson and logarithmic.
Keywords: Discrete Erlang mixtures, moments, cumulant, cumulant generating function, posterior distribution, Poisson, geometric, logarithmic