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Expectation properties of generalized order statistics based on the Gompertz-G family of distributions

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

Operations Research and Decisions

2023

Vol. 33, No. 4

1--14

Gompertz-G family of distributions has been considered. The moment properties of generalized order statistics were studied and characterization results have been presented. Further, several examples and special cases were discussed. The results can be applied to many known distributions included in this family.

Characterisation of some generalised continuous distributions by doubly truncated moments

Athar Haseeb, Ahsanullah Mohammad, Ali Mohd. Almech

Operations Research and Decisions

2023

Vol. 33, No. 1

1--19

The characterisation of probability distribution plays an important role in statistical studies. There are various methods of characterisation available in the literature. The characterisation using truncated moments limits the observations; hence, researchers may save time and cost. In this paper, the characterisation of three general forms of continuous distributions based on doubly truncated moments has been studied. The results are given simply and explicitly. Further, the results have been applied to some well-known continuous distributions.

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.