# A Study of Exponential-Exponential and Exponentiated Inverted Weibull Distributions for Motor Insurance Claim

## Authors

• Sukanda Dankunprasert
• Tosaporn Talangtam

## Keywords:

Maximum likelihood estimation (MLE),, Fixed Point Iteration method, Aggregate Claims

## Abstract

In this paper, we study the modeling of claim severity and compare these models. The models are Exponential-Exponential (EE), Exponentiated Inverted Weibull (EIW) and Exponential (EXP) distributions which are appropriat for motor insurance claims. The claims data sets of individual claims and aggregate claims are considered. The maximum likelihood estimation (MLE) is used for parameters estimation and the goodness of fit test (GOF) is Kolmogorov-Smirnov test (K-S test). We conclude that the EE, EIW and EXP are appropriate for models for the data of individual claims, aggregated claims by day and aggregated claims by month, respectively.

## Author Biographies

### Sukanda Dankunprasert

Mathematics Department, Faculty of Science, Khon Kaen University

### Tosaporn Talangtam

Mathematics Department, Faculty of Science, Khon Kaen University

## References

[1] Flaih A, Elsalloukh H, Mendi E, Milanova M, The Exponentiated Inverted Weibull distribution, Applied Mathematics and Information Sciences, 6, No. 2 (2012), 167-171.

[2] Hogg RV, Craig A and McKean JW. Introduction to Mathematical Statistical. 6th ed. New Jersey: Prentice Hall; 2005.

[3] Klugman SA, Panjer HH, Willmot GE. Loss Models: From Data to Decisions. 3rd ed. New York: John Wiley & Sons; 2008.

[4] Pavel V. Shevchenko, Calculation of aggregate loss distributions, The Journal of Operational Risk, 5, No. 2 (2010), 3-40.

[5] Viera P. Modelling and Simulation in Non-life Insurance: Proceedings of the 5th international conference on Applied mathematics, simulation, modelling; 2011 July 14 – 16; Corfu Island, Greece. USA: Wisconsin: Stevens Point, 2011.

[6] Dankunprasert S. 2017. The Modeling of Claim Severity with Infinite Mixture Models for Individual Data of Motor Insurance. Master of Science Thesis in Applied Mathematics, Graduate School, Khon Kaen University.

2018-06-30

## How to Cite

Dankunprasert, S., & Talangtam, T. (2018). A Study of Exponential-Exponential and Exponentiated Inverted Weibull Distributions for Motor Insurance Claim. Journal of Applied Statistics and Information Technology, 3(1), 48–51. Retrieved from https://ph02.tci-thaijo.org/index.php/asit-journal/article/view/166901

## Section

Research Articles