Abstract
In actuarial science, it is often of interest to compare stochastically extreme claim amounts from heterogeneous portfolios. In this regard, in the present work, we compare the smallest order statistics arising from two heterogeneous portfolios in the sense of the usual stochastic, hazard rate, reversed hazard rate and likelihood ratio orderings. We also consider the multiple-outlier model and obtain some ordering results. It is assumed that the portfolios belong to the general exponentiated location-scale model. The results obtained here are based on vector majorization of parameters and multivariate chain majorization with heterogeneity in different parameters. For the purpose of illustration, the derived results are applied to some well known distributions. Various examples and counterexamples are also provided. Finally, a simulation study is conducted to validate some of the results established here.
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Acknowledgments
The authors are thankful to the Editor and an anonymous referee for some useful comments and suggestions, which have resulted in improving the content and the presentation of the paper. 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. The authors also wish to thank Mr. Subhankar Dutta for his help in the simulation part of this manuscript.
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Das, S., Kayal, S. & Balakrishnan, N. Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models. Methodol Comput Appl Probab 23, 971–999 (2021). https://doi.org/10.1007/s11009-020-09793-y
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DOI: https://doi.org/10.1007/s11009-020-09793-y
Keywords
- Stochastic orderings
- Smallest claim amounts
- Vector majorization
- Multivariate chain majorization
- T-transform matrix
- Exponentiated location-scale model