| Abstract [eng] |
This work is based on two articles: Kahadawala Cooray, Malwane M. A. Amanda, „Modeling actuarial data with a composite lognormal – Pareto model“ (Scandinavian Actuarial Journal, 5, pages 321-334) and McNeil Alexander J. „Estimating the tails of loss severity distributions using extreme value theory“ (ASTIN Bulletin, 27, pages 117-137). The first article presents a two - parameter smooth continuous composite lognormal - Pareto model. The second one analyses generalised Pareto distribution and how does this distribution cover large loses. The purpose of this writing is to mix lognormal and generalised Pareto distributions in to one four parameter smooth continuous distribution. The lognormal distribution is used to model small data with higher frequencies, and the generalised Pareto distribution is used to model large data with low frequencies. In this work we also try to use a modified way of mixing these two distributions than Kahadawala Cooray and Malwane M. A. Amanda used in their work. Writing also includes an analysis of some properties of this model, method of parameter estimation and three data sets analysis based on this distribution. The results show that because of some properties of mixing these two distributions, a composite model is suitable for covering small loses as well as it is suitable for covering large loses. But most important result is that the composite lognormal - generalised Pareto distribution is fit to cover data sets, which include small loses and very large loses also. This type of data is very common in an insurance industry. |
