International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2018, Vol. 3, Issue 4, Part A

Binomial mixture based on generalized four parameter beta distribution as prior


Author(s): Erick Okuto

Abstract: 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.

Pages: 65-73 | Views: 415 | Downloads: 21

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How to cite this article:
Erick Okuto. Binomial mixture based on generalized four parameter beta distribution as prior. International Journal of Statistics and Applied Mathematics. 2018; 3(4): 65-73.
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