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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.

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.

Sharp bounds for the bias of trimmed means of progressively censored order statistics

Bieniek M.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

99--112

We provide sharp upper and lower bounds on the bias of trimmed means of progressively censored type II order statistics from general distributions in various scale units. The results are illustrated with numerical examples. We also discuss this problem for distributions with decreasing density or failure rate, as well as for generalized order statistics.

Tsallis' entropy bounds for generalized order statistics

Kałuszka M., Okolewski A.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

253--262

We present sharp bounds for expectations of generalized order statistics with random indices expressed in terms of Tsallis’ entropy. The bounds are attainable and provide new characterizations of some nontrivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.

Limiting distributions of differences between some generalized order statistics

Bieniek M., Szynal D.

Demonstratio Mathematica

2001

Vol. 34, nr 2

305-314