Mathematics and Statistics Vol. 11(5), pp. 856 - 867
DOI: 10.13189/ms.2023.110513
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Properties and Applications of Klongdee Distribution in Actuarial Science

Adisak Moumeesri ¹, Weenakorn Ieosanurak ^2,*
1 Department of Statistics, Faculty of Science, Silpakorn University, Thailand
² Department of Mathematics, Faculty of Science, Khon Kaen University, Thailand

ABSTRACT

We have introduced a novel continuous distribution known as the Klongdee distribution, which is a combination of the exponential distribution with parameter and the gamma distribution with parameters . We thoroughly examined various statistical properties that provide insights into probability distributions. These properties encompass measures such as the cumulative distribution function, moments about the origin, and the moment-generating function. Additionally, we explored other important measures including skewness, kurtosis, C.V., and reliability measures. Furthermore, we explore parameter estimation using nonlinear least squares methods. The numerical results presented compare the unweighted and weighted least squares (UWLS and WLS) methods, maximum likelihood estimation (MLE), and method of moments (MOM). Based on our findings, the MLE demonstrates superior performance compared to other parameter estimation methods. Moreover, we demonstrate the application of this distribution within an actuarial context, specifically in the analysis of collective risk models using a mixed Poisson framework. By incorporating the proposed distribution into the mixed Poisson model and analyzing a real-life dataset, it has been determined that the Poisson-Klongdee model outperforms alternative models in terms of performance. Highlighting its capability to mitigate the problem of overcharges, the Poisson-Klongdee model has been proven to be a valuable tool.

KEYWORDS
Exponential Distribution, Gamma Distribution, Parameter Estimations, Bonus-malus System, Actuarial Science

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Adisak Moumeesri , Weenakorn Ieosanurak , "Properties and Applications of Klongdee Distribution in Actuarial Science," Mathematics and Statistics, Vol. 11, No. 5, pp. 856 - 867, 2023. DOI: 10.13189/ms.2023.110513.

(b). APA Format:
Adisak Moumeesri , Weenakorn Ieosanurak (2023). Properties and Applications of Klongdee Distribution in Actuarial Science. Mathematics and Statistics, 11(5), 856 - 867. DOI: 10.13189/ms.2023.110513.