Mathematica Eterna
Open Access

Abstract

Modeling fire loss data using mixture of Burr and log-normal distributions

Xiaolin Song

Fire loss data usually has the characters of leptokurtic and fat tail, and it is fitted well by the mixture models. In his paper, we construct mixture of Burr and log-normal distributions. Some related statistical properties are investigated including the analytical expressions for the hazard function, each order moment and the mean deviation. The parameters are estimated via EM algorithm. We illustrate an application to the Chinese fire loss data. The parameter estimation and model checking of simulation data are given using the R language. Finally, we investigate risk measures V aR and T V aR, the theoretical values and empirical values are compared. The results show that the mixture of Burr and log-normal model gives better fit.