EM Algorithm for Poisson-Lindley Distribution
Abstract
Mixed Poisson distributions have been used in scientific fields for modelling non-homogenous
populations, (Karlis and xekalaki, 2005)..
For example, in acturial applications, mixed Poisson distributions are used for modeling
total claims in insurance.
In this work, the concentration is mainly on the estimation of the parameters of Poisson-
Lindley distribution using EM Algorithm which was first introduced by Dempster (1977).
One-parameter, two-parameter and three-parameter Lindley distributions are compounded
by the Poisson distribution to form the Poisson-Lindley distributions and then the parameters
estimated.
In order to carry out the EM Algorithm successfully, the posterior distribution is applied
and the posterior expectation calculated.
Various properties of each distribution are determined, for example, the rth moment, the
cumulative distribution function (cdf), the moment generating function (mgf), the probability
generating function (mgf) and the characteristic function.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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