Šis darbas remiasi dviem straipsniais: Kahadawala Cooray, Malwane M. A. Amanda, „Modeling actuarial data with a composite lognormal – Pareto model“ (Scandinavian Actuarial Journal, 5, 321-334 psl.) ir McNeil Alexander J. „Estimating the tails of loss severity distributions using extreme value theory“ (ASTIN Bulletin, 27, 117-137 psl.). Pirmajame pristatomas sudėtinis lognormalusis – Pareto skirstinys. Antrajame nagrinėjamas apibendrintas Pareto skirstinys, tiriama, kaip jis aprašo dideles žalas. Šio magistro darbo tikslas yra sujungti lognormalųjį bei apibendrintą Pareto skirstinius. Pirmasis jų gerai aprašo mažas žalas su dideliais dažniais, antrasis – dideles, turinčias mažus dažnius. Darbe taip pat naudojamas kiek pakeistas Kahadawala Cooray ir Malwane M. A. Amanda straipsnyje pasiūlytas skirstinių sujungimo būdas. Šiame darbe ištirtos kai kurios sudėtinio lognormaliojo – apibendrinto Pareto skirstinio su keturiais laisvais parametrais savybės, pateiktas įverčių radimo metodas, bei, remiantis šiuo modeliu, išnagrinėtos trys duomenų imtys. Rezultatai rodo jog, dėl tam tikrų sujungimo savybių, modelis tinkamas aprašyti tiek didelėms, tiek mažoms žaloms, o, svarbiausia, mišrioms žaloms, tarp kurių pasitaiko tiek mažų, tiek labai didelių. Pastarojo tipo duomenys gana dažni draudimo praktikoje. / 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... [to full text]
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2008~D_20090908_201800-26222 |
| Date | 08 September 2009 |
| Creators | Kuodis, Gediminas |
| Contributors | Paulauskas, Vygantas, Vilnius University |
| Publisher | Lithuanian Academic Libraries Network (LABT), Vilnius University |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20090908_201800-26222 |
| Rights | Unrestricted |
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