Interval Estimations for the Mean of the Generalized Poisson and Generalized Negative Binomial Distributions |
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Authors: | M Arefi G R Mohtashami Borzadaran Y Vaghei |
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Institution: | 1. Department of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran;2. Department of Statistics and Ordered and Spatial Data Center of Excellence, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran |
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Abstract: | In this article, we extend the Wald, score, skewness-corrected score, likelihood ratio, and mid-P intervals for the means of the generalized Poisson and generalized negative binomial distributions. These distributions are the members of the discrete version of the natural exponential family (NEF) with cubic variance function (CVF). Also, the coverage probabilities, the distal and mesial noncoverage probabilities, and the lengths of the proposed confidence intervals are estimated by means of a Monte Carlo simulation study. Finally, some practical examples are provided to show the applicability of the proposed intervals in applied studies. |
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Keywords: | Confidence interval Coverage probability Cubic variance function (CVF) Generalized negative binomial distribution Generalized Poisson distribution Natural exponential family (NEF) |
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