# Ordering extremes of exponentiated location-scale models with dependent and heterogeneous random samples

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## Abstract

This paper is devoted to some ordering results for the largest and the smallest order statistics arising from dependent heterogeneous exponentiated location-scale random observations. We assume that the sets of observations are sharing a common or different Archimedean copula(s). Sufficient conditions for which the usual stochastic order and the reversed hazard rate order between the extreme order statistics hold are derived. Various numerical examples are provided for the illustration of the proposed results. Finally, some applications of the comparison results in engineering reliability and auction theory are presented.

## Keywords

Archimedean copula Order statistics Majorization Stochastic orders## Mathematics Subject Classification

60E15 62G30 60K10## Notes

### Acknowledgements

The authors would like to thank the Editor in Chief Professor Maria Kateri and three anonymous reviewers for their positive remarks and useful comments. One of the authors, Sangita Das thanks the financial support provided by the MHRD, Government of India. Suchandan Kayal gratefully acknowledges the partial financial support for this research work under a Grant MTR/2018/000350, SERB, India.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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