Negative binomial-Lindley distribution and its application

Hossein Zamani, Noriszura Ismail

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)4-9
Number of pages6
JournalJournal of Mathematics and Statistics
Volume6
Issue number1
Publication statusPublished - 2010

Fingerprint

Negative binomial distribution
Negative Binomial
Count Data
Siméon Denis Poisson
Factorial Moments
Compound Distribution
Reparameterization
Exponential Family
Method of Moments
Maximum Likelihood Estimation
Insurance
Parameter Estimation
Count
Closed-form
Zero
Modeling

Keywords

  • Count data
  • Insurance
  • Mixed negative binomial
  • Negative binomial-Lindley

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Negative binomial-Lindley distribution and its application. / Zamani, Hossein; Ismail, Noriszura.

In: Journal of Mathematics and Statistics, Vol. 6, No. 1, 2010, p. 4-9.

Research output: Contribution to journalArticle

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