Analysis of discrete data by Conway-Maxwell Poisson distribution. (English) Zbl 1443.62045
Summary: In this paper, we further study the Conway-Maxwell Poisson distribution having one more parameter than the Poisson distribution and compare it with the Poisson distribution with respect to some stochastic orderings used in reliability theory. Likelihood ratio test and the score test are developed to test the importance of this additional parameter. Simulation studies are carried out to examine the performance of the two tests. Two examples are presented, one showing overdispersion and the other showing underdispersion, to illustrate the procedure. It is shown that the COM-Poisson model fits better than the generalized Poisson distribution.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 62N05 | Reliability and life testing |
| 60E15 | Inequalities; stochastic orderings |
| 62F03 | Parametric hypothesis testing |
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