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

Athar Haseeb, Alharbi Yousef F., Fawzy Mohamad A.

Operations Research and Decisions

2022

Vol. 32, No. 4

17--31

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.

Characterizations of the exponential distribution by geometric compound

Iwińska M., Popowska B.

Fasciculi Mathematici

2011

Nr 47

5--10

Under the reliability conditions IFRA/DFRA (NBU/ NWU), the exponential distribution is characterized by stochas- tic ordering properties which link the geometric compound with record values (spacing of record values). The index of record val- ues is random.

On the fractional record values

Bieniek M., Szynal D.

Probability and Mathematical Statistics

2004

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.