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Binomial Mixture Based on Generalized Four Parameter Beta Distribution as Prior

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Publication Date
6/10/2018
Author
Okuto, Erick
Type
Article
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Abstract/Overview

A probability distribution can be constructed by mixing two distributions. Binomial distribution when compounded with beta distribution as prior forms a binomial mixture that is a continuous distribution. Skellam 1948, mixed a binomial distribution with its parameter being the probability of success considered as a random variable taking beta distribution. Probability distributions with binomial outcome tend to fail to fit empirical data due to over-dispersion. To address this challenge binomial mixtures are modeled to cater for the influence caused by over-dispersion. This paper focuses on binomial mixture with a four parameter generalized beta mixing distributions. In particular it focuses on application of McDonald generalized and Gerstenkon generalized mixing distributions. The binomial mixture obtained is proved to be a probability density function. Its moments are obtained using probability generating function techniques. The binomial mixture obtained can be applicable to probability distributions whose outcome are binomial in nature.

Subject/Keywords
Probability distribution; Binomial mixture; Four parameter generalized beta distribution; Over-dispersion; Moments
Publisher
International Journal of Statistics and Applied Mathematics
ISSN
2456-1452
Permalink
http://ir.jooust.ac.ke:8080/xmlui/handle/123456789/9382
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