Hürlimann, Werner General location transform of the order statistics from the exponential, Pareto and Weibull, with application to maximum likelihood estimation. (English) Zbl 1019.62043 Commun. Stat., Theory Methods 29, No. 11, 2535-2545 (2000). 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. Cited in 2 Documents 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 Keywords:normalizing transforms; analytical method; reinsurance Citations:Zbl 0507.62008 PDFBibTeX XMLCite \textit{W. Hürlimann}, Commun. Stat., Theory Methods 29, No. 11, 2535--2545 (2000; Zbl 1019.62043) Full Text: DOI References: [1] Ammeter H., Quarterly letter algemeene reinsurance companies, Jubilee number 2 pp 79– (1964) [2] Dempster A.P., Journal Royal Statistical Society 39 pp 1– (1977) [3] DOI: 10.1214/aos/1176345777 · Zbl 0507.62008 · doi:10.1214/aos/1176345777 [4] Huang J., Scandinavian Actuarial Journal 10 pp 187– (1975) [5] Keller B., Bulletin Swiss Association of Actuaries 10 pp 203– (1991) [6] Kluppelberg C., Bulletin Swiss Association of Actuaries 10 pp 29– (1994) [7] Kluppelberg C., Blatter der Deutschen Gesellschaft fur Versicherungsmathematik 21 pp 213– (1993) [8] Kremer E., Einfuhrung in die Versicherungsmathematik (1985) · Zbl 0578.62089 [9] DOI: 10.2143/AST.28.2.519069 · Zbl 1162.91420 · doi:10.2143/AST.28.2.519069 [10] DOI: 10.1111/1467-9868.00082 · doi:10.1111/1467-9868.00082 [11] Panjer H.H., Insurance Risk Models (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.