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A general method of computing mixed Poisson probabilities by Monte Carlo sampling

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  • Ong, Seng-Huat
  • Lee, Wen-Jau
  • Low, Yeh-Ching

Abstract

Mixed Poisson distributions form an important class of distributions in applications. However, the application of many of these mixed Poisson distributions is hampered by the complicated probability distributions. The paper examines Monte Carlo sampling as a general technique for computation of mixed Poisson probabilities which is applicable to any mixed Poisson distribution with arbitrary mixing distribution. The accuracy and computational speed of this method is illustrated with the Poisson–inverse Gaussian distribution. The proposed method is then applied to compute probabilities of the Poisson–lognormal distribution, a popular species abundance model. It is also shown that in the maximum likelihood estimation of Poisson–lognormal parameters by E–M algorithm, the application of the proposed Monte Carlo computation in the algorithm avoids numerical problems.

Suggested Citation

  • Ong, Seng-Huat & Lee, Wen-Jau & Low, Yeh-Ching, 2020. "A general method of computing mixed Poisson probabilities by Monte Carlo sampling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 98-106.
    • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:98-106
    DOI: 10.1016/j.matcom.2019.09.003
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    1. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    2. Goro Ishii & Reiko Hayakawa, 1960. "On the compound binomial distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(1), pages 69-80, February.
    3. S. H. Ong & P. A. Lee, 1985. "On the bivariate negative binomial distribution of mitchell and paulson," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(3), pages 457-465, August.
    4. R. C. H. Cheng, 1977. "The Generation of Gamma Variables with Non‐Integral Shape Parameter," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 71-75, March.
    5. M. Holla, 1967. "On a poisson-inverse gaussian distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 11(1), pages 115-121, December.
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    1. Sedighizadeh, Davoud & Masehian, Ellips & Sedighizadeh, Mostafa & Akbaripour, Hossein, 2021. "GEPSO: A new generalized particle swarm optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 194-212.

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