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General location transform of the order statistics from the exponential, Pareto and Weibull, with application to maximum likelihood estimation. (English) Zbl 1019.62043

Summary: Based one some common distribution properties of order statistics and the transformation theory of B. Efron [Ann. Stat. 10, 323-339 (1982; Zbl 0507.62008)], 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.

MSC:

62G30 Order statistics; empirical distribution functions
62F12 Asymptotic properties of parametric estimators
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E10 Characterization and structure theory of statistical distributions

Citations:

Zbl 0507.62008
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References:

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