Date of Award

2015

Publisher

North Dakota State University

Document Type

Thesis

Degree Awarded

Master of Science (MS)

Program

Statistics

Department

Statistics

College

Science and Mathematics

Faculty Advisor

Miljkovic, Tatjana

Description

Property and Casualty insurance companies set premium rates by evaluating both loss fre- quency and loss severity data. Insurance companies often model severity using a well-known single distribution such as Lognormal or Gamma etc. Alternatively, they may use a composite distri- bution, such as a Gamma-Lognormal. Both approaches assume that the data are homogeneous. Real data may exhibit some behavior such as multimodality or irregular shape suggesting that they are heterogeneous. In that case, in order to appropriately model the dataset, a model that is a composite of several distributions of the same family is needed. This thesis proposes tting sever- ity of losses using mixtures of Lognormal distributions via the Expectation Maximization (EM) algorithm. The capability of this procedure is demonstrated through the use of a simulation study before it is used on real data. For modeling the Danish Fire loss dataset a 4-component nite mixture model of Lognormal distributions is proposed.

Rights

NDSU Policy 190.6.2

Rights Link

https://www.ndsu.edu/fileadmin/policy/190.pdf

Handle Identifier

https://hdl.handle.net/10365/27861

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