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

Das, Sangita; Kayal, Suchandan

doi:10.1007/s00184-019-00753-2

“…By using an approach similar to the one used in Theorem 3.2, the following theorem can be established by using Theorem 3.6 of Das and Kayal [7]. So, the proof is omitted here for conciseness.…”

Section: Remark 32mentioning

confidence: 99%

“…The general exponentiated location-scale model serves this purpose very well due to its great flexibility. Das et al [9], Das and Kayal [7] and Das et al [8] considered (1.1) to obtain different stochastic ordering results.…”

Section: Introductionmentioning

confidence: 99%

Ordering results for smallest claim amounts from two portfolios of risks with dependent heterogeneous exponentiated location-scale claims

Das¹,

Kayal²

2021

Prob. Eng. Inf. Sci.

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Let $\{Y_{1},\ldots ,Y_{n}\}$ be a collection of interdependent nonnegative random variables, with $Y_{i}$ having an exponentiated location-scale model with location parameter $\mu _i$ , scale parameter $\delta _i$ and shape (skewness) parameter $\beta _i$ , for $i\in \mathbb {I}_{n}=\{1,\ldots ,n\}$ . Furthermore, let $\{L_1^{*},\ldots ,L_n^{*}\}$ be a set of independent Bernoulli random variables, independently of $Y_{i}$ 's, with $E(L_{i}^{*})=p_{i}^{*}$ , for $i\in \mathbb {I}_{n}.$ Under this setup, the portfolio of risks is the collection $\{T_{1}^{*}=L_{1}^{*}Y_{1},\ldots ,T_{n}^{*}=L_{n}^{*}Y_{n}\}$ , wherein $T_{i}^{*}=L_{i}^{*}Y_{i}$ represents the $i$ th claim amount. This article then presents several sufficient conditions, under which the smallest claim amounts are compared in terms of the usual stochastic and hazard rate orders. The comparison results are obtained when the dependence structure among the claim severities are modeled by (i) an Archimedean survival copula and (ii) a general survival copula. Several examples are also presented to illustrate the established results.

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“…To the best of our knowledge, stochastic comparisons of the largest claim amounts when random claims have ELS models have not been addressed in the literature so far. However, some generalized models to study ordering properties of extreme order statistics in the context of reliability studies can be found in [7][8][9][10][11]16]. In this paper, we address this problem and derive sufficient conditions for the stochastic comparison of the largest claim amounts in the sense of various stochastic orderings.…”

Section: Introductionmentioning

confidence: 99%

Ordering results between the largest claims arising from two general heterogeneous portfolios

Das

¹

,

Kayal

²

2021

Filomat

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This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general family of distributions. The largest claims have been compared based on various stochastic orderings. The established sufficient conditions are associated with the matrices and vectors of model parameters. Applications of the results are provided for the purpose of illustration.

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“…To the best of our knowledge, stochastic comparisons of the largest claim amounts when random claims have ELS models have not been addressed in the literature so far. However, some generalized models were considered by Das and Kayal (2019a), Das and Kayal (2019b) and Das et al (2019) to study ordering properties of extreme order statistics in the context of reliability studies. In this paper, we address this problem and derive sufficient conditions for the stochastic comparison of the largest claim amounts in the sense of various stochastic orderings.…”

Section: Introductionmentioning

confidence: 99%

Ordering results between the largest claims arising from two general heterogeneous portfolios

Das¹,

Kayal²

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general family of distributions. The largest claims have been compared based on various stochastic orderings. The established sufficient conditions are associated with the matrices and vectors of model parameters. Applications of the results are provided for the purpose of illustration.

show abstract

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

Cited by 16 publications

References 32 publications

Ordering results for smallest claim amounts from two portfolios of risks with dependent heterogeneous exponentiated location-scale claims

Ordering results for smallest claim amounts from two portfolios of risks with dependent heterogeneous exponentiated location-scale claims

Ordering results between the largest claims arising from two general heterogeneous portfolios

Ordering results between the largest claims arising from two general heterogeneous portfolios

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