Abstract: 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.
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Keywords and phrases: special functions, Erlang distribution, Erlang mixture, moments, Laplace transform, Erlang parameter, posterior, Bayes estimate.
Received: January 25, 2023; Revised: December 15, 2023; Accepted: February 10, 2024; Published: March 23, 2024
How to cite this article: Beatrice M. Gathongo, Isaac C. Kipchirchir and Joseph I. Mwaniki, Continuous Erlang mixed distributions and their properties, Far East Journal of Theoretical Statistics 68(1) (2024), 165-180. http://dx.doi.org/10.17654/0972086324010
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