A new count data model applied in the analysis of vaccine adverse events and insurance claims


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 22 , ISSUE 3 (September 2021) > List of articles

A new count data model applied in the analysis of vaccine adverse events and insurance claims

Showkat Ahmad Dar * / Anwar Hassan / Ahmad Para Bilal / Sameer Ahmad Wani

Keywords : poisson distribution, weighted exponential distribution, compound distribution, count data, maximum likelihood estimation

Citation Information : Statistics in Transition New Series. Volume 22, Issue 3, Pages 157-174, DOI: https://doi.org/10.21307/stattrans-2021-032

License : (CC BY-NC-ND 4.0)

Received Date : 24-February-2020 / Accepted: 07-October-2020 / Published Online: 05-September-2021



The article presents a new probability distribution, created by compounding the Poisson distribution with the weighted exponential distribution. Important mathematical and statistical properties of the distribution have been derived and discussed. The paper describes the proposed model’s parameter estimation, performed by means of the maximum likelihood method. Finally, real data sets are analyzed to verify the suitability of the proposed distribution in modeling count data sets representing vaccine adverse events and insurance claims.

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Berreto-Souza, W., Bakouch, H., (2013). A new lifetime model with decreasing failure rate. A journal of theoretical and Applied Statistics, 47(2), pp. 465–476.

Hajebi, M., Rezaei, S. and Nadarajah, S., (2013). An exponential- negative binomial distribution. REVSTAT-Statistical journal, 11(2), pp. 191–210.

Asgharzadeh, A., Bakouch, H.S., Nadarajah, S. and Esmaeili, L., (2014). A new family of compound lifetime distributions. Kybernetika, 50, pp. 142–169.

Mohmoudi, E. Jafari, A. A., (2014). The compound class of linear failure rate power series distributions: model, properties and applications. Communications in statistics-simulation and computation.

Silva, R. B., Cordeiro, G. M., (2015). The Burr XII power series distribution: A new compounding family. The Brazilian journal of probability and statistics, 29, pp. 565–589.

Pinho, L. G. B., Cordeiro, G. M. and Nobre, J. S., (2015). On the Harris-G class of distributions: general results and application. Brazilian journal of probability and statistics, 29(4), pp. 813–832.

Bourguignon, M., Silva, R. B. and Cordeiro, G. M., ( 2014). Anew class of fatigue life distributions. Journal of statistics Computation and Simulation,84 , pp. 2619–2635.

Bordbar, F., Nematollahi, A. R., (2016). The modified exponential- geometric distribution. Communications in Statistics –Theory and Methods, 45(1), pp. 173– 181.

Flores, D, J., Borges, P., Cancho, G. and Louzada, F., (2013). The complementary exponential power series distribution. Brazilian journal of probability and statistics, 27, pp. 565–584.

Ghitany M. E., Alqallaf F., Al- Mutairi D. K. and Husain H. A.,(2011). A two parameter weighted Lindley distribution and its applications to survival data, Mathematics and Computers in Simulations, 81, pp. 1190–1201.

Christophe Chesneau, Hassan S. Bakouch, Tassaddaq Hussain and Bilal A. Para, (2020). The cosine geometric distribution with count data modeling, Journal of Applied Statistics, DOI: 10.1080/02664763.2019.1711364.

R Core Team, (2019). R version 3.5.3: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

Klugman S., Panjer H., Willmot G., (2012). Loss Models. From Data to Decisions. John Wiley and Sons, New York.

C. E. Rose, S. W.Martin, K. A. Wannemuehler, and B. D. Plikaytis, (2006). On the use of zero infilated and hurdle models for modeling vaccine adverse events count data, Journal of Biopharmaceutical Statistics, Vol. 16, pp. 463–481.