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Characterizations of power distributions via moments of order statistics and record values

100%

Grudzień Z. , Szynal D.

nr 4

467-475

Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.

On the fractional record values

100%

Bieniek M. , Szynal D.

tom Vol. 24, Fasc. 1

27--46

We define the record-values process which may be considered as the collection of record values with non-integer or fractional indices. The alternative con-struction from the sample as well as the basic properties of the defined process are shown.

Relations for moments of generalised order statistics based on Weibull–G family of distributions

88%

Athar H. , Alharbi Y. F. , Fawzy M. A.

tom 32

nr 4

The Weibull distribution is one of the important distributions used in reliability theory and life-testing experiments. The generalised versions of the Weibull distribution give a more flexible model for these studies. The Weibull–G family of distributions is one of the extended versions extensively studied. In this paper, we have studied moments properties of generalised order statistics for the said distribution in terms of a single moment, product moments and characterisation. Several examples and special cases are presented. The results can be applied to all distributions belonging to this family.