Mathematics and Statistics Vol. 11(2), pp. 405 - 420
DOI: 10.13189/ms.2023.110220
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Actuarial Measures, Estimation and Applications of Sine Burr III Loss Distribution

John Abonongo ^1,*, Ivivi J. Mwaniki ², Jane A. Aduda ^3
1 Institute for Basic Sciences, Technology and Innovation, Pan African University, Kenya
² School of Mathematics, Statistics and Actuarial Science Division, University of Nairobi, Kenya
³ Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Kenya

ABSTRACT

The usefulness of heavy-tailed distributions for modeling insurance loss data is arguably an important subject for actuaries. Appropriate use of trigonometric functions allows a good understanding of the mathematical properties, limits over parameterization, and gives better applicability in modeling different datasets. Thus, the proposed method ensures that no additional parameter(s) is/are introduced in the bit to make a distribution from the F-Loss family of distributions flexible. The purpose of this paper is to improve the flexibility of the F-Loss family of distributions without introducing any additional parameter(s) and to develop heavy-tailed distributions with fewer parameters that give a better parametric fit to a given dataset than other existing distributions. In this paper, a new heavy-tailed distribution known as sine Burr III Loss distribution is proposed using the sine F-Loss generator. This distribution is flexible and able to model varying shapes of the hazard rate compared with the traditional Burr III distribution. The densities exhibit different kinds of decreasing and right-skewed shapes. The hazard rate functions show different kinds of decreasing, increasing constant-decreasing, and upside-down bathtub shapes. The statistical properties and actuarial measures are studied. The skewness is always positive, and the kurtosis is increasing. The numerical values of the actuarial measures show that increasing confidence levels are associated with increasing VaR, TVaR, and TV. The maximum likelihood estimators are studied, and simulations are carried out to ascertain the behavior of the estimators. It is observed that the estimators are consistent. The usefulness of the proposed distribution is demonstrated with two insurance loss datasets and compared with other known classical heavy-tailed distributions. The results show that, the proposed distribution provides the best parametric fit for the two insurance loss datasets. Insurance practitioners can employ the proposed models in modeling insurance loss since they are flexible.

KEYWORDS
Sine F-Loss, Burr III, Heavy-tailed Distribution, Insurance Loss, Maximum Likelihood Estimation, Actuarial Measures

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] John Abonongo , Ivivi J. Mwaniki , Jane A. Aduda , "Actuarial Measures, Estimation and Applications of Sine Burr III Loss Distribution," Mathematics and Statistics, Vol. 11, No. 2, pp. 405 - 420, 2023. DOI: 10.13189/ms.2023.110220.

(b). APA Format:
John Abonongo , Ivivi J. Mwaniki , Jane A. Aduda (2023). Actuarial Measures, Estimation and Applications of Sine Burr III Loss Distribution. Mathematics and Statistics, 11(2), 405 - 420. DOI: 10.13189/ms.2023.110220.