ESTIMATING LOSS SEVERITY DISTRIBUTION: CONVOLUTION APPROACH | Science Publications

Journal of Mathematics and Statistics

ESTIMATING LOSS SEVERITY DISTRIBUTION: CONVOLUTION APPROACH

Ro J. Pak

DOI : 10.3844/jmssp.2014.247.254

Journal of Mathematics and Statistics

Volume 10, Issue 2

Pages 247-254

Abstract

Financial loss can be classified into two types such as expected loss and unexpected loss. A current definition seeks to separate two losses from a total loss. In this article, however, we redefine a total loss as the sum of expected and unexpended losses; then the distribution of loss can be considered as the convolution of the distributions of both expected and unexpended losses. We propose to use a convolution of normal and exponential distribution for modelling a loss distribution. Subsequently, we compare its performance with other commonly used loss distributions. The examples of property insurance claim data are analyzed to show the applicability of this normal-exponential convolution model. Overall, we claim that the proposed model provides further useful information with regard to losses compared to existing models. We are able to provide new statistical quantities which are very critical and useful.

Copyright

© 2014 Ro J. Pak. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.