Statistics Masters Theses

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Modeling Loss Severity With Lognormal Mixtures
(North Dakota State University, 2015) Hugen, Joshua Gilbert
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.