B54: Fitting Mixture Models to Right-Censored Data

Modeling Right-Censored Danish Fire Loss Data

A dataset is right-censored at a censoring point if, whenever observations are greater than the censoring point, they are recorded as being equal to the censoring point; otherwise, they are recorded as their true values. Such data occur in insurance losses when a policy contains a maximum benefit. This presents a challenge for modeling since the true values of censored observations are unavailable. In this project, we use the Expectation Maximization (EM) algorithm to find the best mixture model to fit the right-censored Danish Fire Loss data. We look at mixtures containing each combination of up to two lognormal, Weibull, and gamma distributions, and compare model fits on the basis of AIC. This approach yields a 2-component lognormal mixture as the best fit. Then, a simulation study is conducted to verify the accuracy of parameter estimates using the EM algorithm. Future research may focus on fitting right-censored mixture models with three components and techniques for eliminating spurious solutions. This research also applies to our future careers in the data science and actuarial science fields. Both fields deal with right-censored data, and this approach using the EM algorithm will be valuable for fitting models in such situations.

Author: Jake Cowan and Caitlin Ryder

Faculty Advisors: Tatjana Miljkovic, Department of Statistics