Statistical Analysis for the Inverse Trinomial Distribution |
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| Authors: | Y. N. Phang S. Z. Sim S. H. Ong |
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| Affiliation: | 1. Faculty of Computer Science and Mathematics, UiTM Cawangan Melaka , Alor?Gajah , Melaka , Malaysia;2. Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Genting, Kelang, Setapak , Kuala Lumpur , Malaysia;3. Institute of Mathematical Sciences , University of Malaya , Kuala Lumpur , Malaysia;4. Institute of Mathematical Sciences , University of Malaya , Kuala Lumpur , Malaysia |
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| Abstract: | This article considers parameter estimation, goodness of fit, likelihood ratio and score tests, and model selection by Akaike information criterion for the inverse trinomial (IT) distribution, a classical one-dimensional random walk distribution. The IT distribution has a cubic variance function of the mean and is a generalization of the negative binomial distribution. Basic distributional properties and expressions for the probability mass function, recurrence formula, moments, and score functions are also presented. |
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| Keywords: | AIC Cubic variance function Goodness of fit Grid search Likelihood ratio Maximum likelihood Negative binomial Overdispersion Parameter estimation Probability generating function Random walk Score test Simulated annealing Zero and first frequencies |
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