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Zero-modified Poisson-Modification of Quasi Lindley distribution and its application

Author

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  • Tharshan Ramajeyam

    (Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka & Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka .)

  • Wijekoon Pushpakanthie

    (Department of Statistics and Computer Science, University of Peradeniya, Peradeniya, Sri Lanka .)

Abstract

The Poisson-Modification of Quasi Lindley (PMQL) distribution is a newly introduced mixed Poisson distribution for over-dispersed count data. The aim of this article is to introduce the Zero-modified PMQL (ZMPMQL) distribution as an alternative to the PMQL distribution in order to accommodate zero inflation/deflation. The method of obtaining the ZMPMQL distribution jointly with some of its important properties, namely the probability mass and distribution functions, mean, variance, index of dispersion, and quantile function are presented. Furthermore, some of its special cases are discussed. The maximum likelihood (ML) estimation method is used for the unknown parameter estimation. A simulation study is conducted in order to evaluate the asymptotic theory of the ML estimation method and to show the superiority of the ML method over the method of moments estimation. The applicability of the introduced distribution is illustrated by using a real-world data set.

Suggested Citation

  • Tharshan Ramajeyam & Wijekoon Pushpakanthie, 2022. "Zero-modified Poisson-Modification of Quasi Lindley distribution and its application," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 113-128, December.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:113-128:n:9
    DOI: 10.2478/stattrans-2022-0045
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    References listed on IDEAS

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    1. Rama Shanker, 2016. "Sujatha Distribution And Its Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 391-410, September.
    2. R. Shanker, 2016. "Sujatha Distribution and its Applications," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 391-410, September.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    4. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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