CONTINUOUS ERLANG MIXED DISTRIBUTIONS AND THEIR PROPERTIES
Beatrice M. Gathongo, Isaac C. Kipchirchir, Joseph I. Mwaniki · Far East Journal of Theoretical Statistics · 2024
In this paper, we determine the formulae for the construction of continuous Erlang mixed distribution (Erlang mixture) and its properties, namely; moments, variance, skewness, kurtosis, Laplace transform, posterior distribution and Bayes estimate of the Erlang distribution parameter. For selected mixing distributions the derived formulae for Erlang mixture and its properties are applied. In particular, the Erlang mixtures are expressible in terms of special functions, namely; beta function, modified Bessel function of the third kind and the Tricomi confluent hypergeometric function. Received: January 25, 2023Revised: December 15, 2023Accepted: February 10, 2024