Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models

Sangita Das (), Suchandan Kayal () and N. Balakrishnan ()
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Sangita Das: National Institute of Technology Rourkela
Suchandan Kayal: National Institute of Technology Rourkela
N. Balakrishnan: McMaster University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 971-999

Abstract: 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.

Keywords: Stochastic orderings; Smallest claim amounts; Vector majorization; Multivariate chain majorization; T-transform matrix; Exponentiated location-scale model; 60E15; 62G30; 60K10; 90B25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09793-y

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