Negative Binomial-Lindley Distribution and Its Application

By Hossein Zamani, Noriszura Ismail. 2010

152 citations recorded by the source corpus.

Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed negative binomial, provided better fit compared to other distributions. Approach: In this study, we introduce a new mixed negative binomial distribution by mixing the distributions of negative binomial (r,p) and Lindley (θ), where the reparameterization of p = exp(-λ) is considered. Results: The closed form and the factorial moment of the new distribution, i.e., the negative binomial-Lindley distribution, are derived. In addition, the parameters estimation for negative binomial-Lindley via the method of moments (MME) and the Maximum Likelihood Estimation (MLE) are provided. Conclusion: The application of negative binomial-Lindley distribution is carried out on two samples of insurance data. Based on the results, it is shown that the negative binomial-Lindley provides a better fit compared to the Poisson and the negative binomial for count data where the probability at zero has a large value.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bf77bba0cd74c52b4c68c944a42031c619ed0e8a

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In Management Science and Operations Research

1. S. Aryuyuen
2. Winai Bodhisuwan

In Statistics and Probability

1. S. Geedipally
2. S. Aryuyuen
3. D. Lord
4. Winai Bodhisuwan

Citations in the corpus

• The Negative Binomial-Generalized Exponential (NB-GE) Distribution (2013, methodology): “In this sense, we are looking for a more flexible alternative to the Poisson distribution, especially under the overdispersion, the NB distribution [13] obtained as a mixture of Poisson and gamma distributions, NB-exponential distribution [12], NB-Pareto distribution [8], NB-inverse Gaussian distrib”
• Developing a Random Parameters Negative Binomial-Lindley Model to analyze highly over-dispersed crash count data (2018, methodology): “Although the Lindley distribution has a closed form (Zamani and Ismail 2010), the Lindley distribution cannot be mixed with the NB distribution in the context of GLM because it is not available in any standard statistical software (e.”
• On the Bayesian estimation of the weighted Lindley distribution (2015, unknown): “Zamani and Ismail [8] introduced Negative Binomial distribution as an alternative to zero-truncated Poisson–LD.”