Skew T and skew normal distributions in modelling insurance loss and reliability data - Vo, Phuoc Hiep (2011)
In this project, we study univariate Skew Normal distribution and univariate Skew t-distribution in modelling skewed data that arise very commonly in loss modelling and reliability analysis. The performances of these two distributions are compared against Gamma, Weibull and Lognormal, which are three popularly used distributions in the above fields. The main findings of our present study show that univariate Skew t-distribution cannot be adequately described by Gamma, Weibull and Lognormal distributions. It is also shown that univariate Skew t-distribution is capable of fitting data generated from other distributions reasonably well; in particular, it is superior to other distributions in fitting highly skewed data. Applications to real life data show that univariate Skew t-distribution is a worthwhile candidate to be considered in modelling highly skewed insurance loss data. On the other hand, for simulating lightly skewed data, univariate Skew Normal distribution can be a reasonably good choice. Applications to real life data show that univariate Skew Normal distribution is promising in analysing reliability data which are typically less skewed than insurance loss data.