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CONTINUOUS ERLANG MIXED DISTRIBUTIONS AND THEIR PROPERTIES
Keywords:
special functions, Erlang distribution, Erlang mixture, moments, Laplace transform, Erlang parameter, posterior, Bayes estimateDOI:
https://doi.org/10.17654/0972086324010Abstract
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, 2023
Revised: December 15, 2023
Accepted: February 10, 2024
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