General location transform of the order statistics from the exponential, pareto and weibull, with application to maximum likelihood estimation

Abstract

Based one some common distribution properties of the order statistics and the transformation theory by Efron(1982), we determine unified explicit general location transformations, which map the distributions of the order statistics from the Exponential, Pareto and Weibull to a standard normal distribution. This result is used to derive analytical formulas for the maximum likelihood estimators of the shape parameter of these distributions of order statistics. The presented exact method is applied to catastrophe earthquake life reinsurance.

Keywords:

• normalizing transform
• analytical method
• reinsurance