Draudimo matematikoje modeliuojant žalas dažnai naudojami dviejų parametrų lognormalusis ir Pareto skirstiniai. Lognormalusis skirstinys taikomas mažoms žaloms su dideliu dažniu aprašyti, o Pareto – didelėms su mažu. Siekiant, kad skirstinys vienodai gerai aprašytu visų tipų žalas, sudaromas nupjauto lognormaliojo ir Pareto skirstinių mišinys su trimis laisvais parametrais. Šis darbas parašytas remiantis Kahadawala Cooray ir Malwane M. A. Ananda straipsniu "Modeling actuarial data with a composite lognormal – Pareto model" ("Scandinavian Actuarial Journal", 2005, 5, 321 - 334 psl.), kuriame nagrinėjamas sudėtinis lognormalusis – Pareto skirstinys. Darbe nagrinėjami lognormalusis ir Pareto skirstiniai, aptariama, kodėl jie turėtų būti naudojami kartu kaip mišinys, pateikiamas nupjauto lognormaliojo ir Pareto skirstinių mišinio tankio funkcijos išvedimas, grafiškai iliustruojamas jos kitimas, priklausomai nuo parametrų parinkimo. Praktinėje dalyje nagrinėjamos trys imtys: sudėtiniu lognormaliuoju – Pareto skirstiniu modeliuoti duomenys, vienos Lietuvos draudimo bendrovės draudimo nuo nelaimingų atsitikimų žalos ir Danijos gaisrų draudimo žalos. Didžiausio tikėtinumo metodu skaitiškai įvertinami mišinio parametrai kiekvienai imčiai, gauti rezultatai lyginami su sudėtinio lognormaliojo – Pareto, lognormaliojo, Pareto, Gama, Weibull skirstinių didžiausio tikėtinumo įverčiais. Palyginimui naudojami Kolmogorovo – Smirnovo, Andersono – Darlingo kriterijai ir chi kvadrato suderinamumo... [toliau žr. visą tekstą] / In insurance mathematics are often used the lognormal ant the Pareto distributions with two parameters to model loss data. The lognormal distribution is used to model small data with higher frequencies, while the Pareto distribution is used to model large data with low frequencies. In order to achieve both of these losses in one model, the truncated lognormal and the Pareto distributions mixture with three parameter is presented. This work is written with reference to Kahadawala Cooray ir Malwane M. A. Ananda article "Modeling actuarial data with a composite lognormal – Pareto model" ("Scandinavian Actuarial Journal", 2005, 5, 321 - 334 pages), where composite lognormal – Pareto model is researched. In this work the necessity of the lognormal and the Pareto distributions mixture is discussed, the derivation of the truncated lognormal and the Pareto distributions mixture model are presented and behaviour of density function in dependent of parameter variation is discussed by illustrating. For practical application three data sets are chosen: simulated from the composite lognormal – Pareto distribution, personal accident insurance loss of one Lithuania insurance company, Danish fire loss data. For the each of data sets the parameters are estimated using maximum likelihood function, resulted estimators are compared with maximum likelihood estimators of composite lognormal – Pareto, lognormal, Pareto, Gamma and Weibull distributions. In order to compare the models the following... [to full text]

Pažeminiai miško gaisrai padidino samanų dangos rūšinę sudėtį. Na ir Nb augaviečių gaisravietėse nustatytos 11 samanų rūšių, o kontroliniuose medynuose – 5 rūšys. Dėl gaisrų atsirado 8, o išnyko 2 samanų rūšys. / The composition of cover moss species was increased by ground-level fire. There were established 11 species of moss in Na and Nb habitats fireplaces and 5 species in control stands. Because of fire appeared 8 species of moss and disappeared 2 species of moss.

The main purpose of the Master paper is to make fire investigations analysis, to find its problems ant find a way to solve them. Also suggest new alternative fire investigation methods. In the first part of my work I studied fire investigation analysis disputed all the methods of fire investigation used in Lithuania. I found and disputed limitations of fire investigation methods and found few solutions for them. I describe new alternative fire investigation methods used abroad. In the second part of my work I have analyzed new fire investigation method- fire dynamic simulator. I Studied principles and use opportunities of FDS- MOKEWIEV and SMARTFIRE programs. In the third part I wrote few concrete examples when these two fire dynamic simulation programs were used. I have also described test computation with SMARTFIRE fire dynamic simulator. I have wrote conclusions and suggested about fire investigation.