Likelihood ratio and dispersive orders for smallest order statistics and smallest claim amounts from heterogeneous Weibull sample

Barmalzan, Ghobad; Najafabadi, Amir T. Payandeh; Balakrishnan, N.

doi:10.1016/j.spl.2015.11.009

Cited by 24 publications

(24 citation statements)

References 5 publications

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“…One interesting issue is to look into the influences of heterogeneity among components and random shocks on the lifetimes of k ‐out‐of‐ n systems. For the case of series system ( k = n ), Barmalzan and Payandeh Najafabadi focused on the heterogeneity among the scale parameters of Weibull components according to the convex transform and right‐spread orderings, and Barmalzan et al established the likelihood ratio and dispersive ordering results in this setting. Afterwards, Barmalzan et al carried out stochastic comparisons between two series systems subject to random shocks in the sense of the usual stochastic and hazard rate orderings when the components have scaled lifetimes.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the results derived by Barmalzan et al, we assume that the distribution functions of the components' lifetimes are of the semiparametric form, ie, the distribution is indexed by a parameter but its explicit form is unknown. Similar with Balakrishnan et al, we use row weak multivariate majorization order to characterize the heterogeneity among components and their surviving probabilities from random shocks.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On fail‐safe systems under random shocks

Zhang

Amini-Seresht

Zhao

2018

Appl Stoch Models Bus & Ind

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In practical situations, systems often suffer shocks from external stressing environments, stressing the system at random. These random shocks may have non-ignorable effects on the system's reliability. In this paper, we provide sufficient (and necessary) conditions on components' lifetimes and their surviving probabilities from random shocks for comparing the lifetimes of two fail-safe systems by means of the usual stochastic, hazard rate, and likelihood ratio orderings. Numerical examples are presented to highlight these theoretical results as well. KEYWORDS fail-safe system, majorization, random shocks, second-price reverse auction, stochastic orders Appl Stochastic Models Bus Ind. 2019;35: 591-602.wileyonlinelibrary.com/journal/asmb

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On fail‐safe systems under random shocks

Zhang

Amini-Seresht

Zhao

2018

Appl Stoch Models Bus & Ind

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“…. , Y n ) in two portfolios, have been discussed by many researchers in literature; see, e.g., Karlin and Novikoff (1963), Ma (2000), Frostig (2001), Hu and Ruan (2004), Denuit and Frostig (2006), Khaledi and Ahmadi (2008), Zhang and Zhao (2015), , Li and Li (2016), Barmalzan et al (2018), , Barmalzan et al (2016), Barmalzan et al (2017), Balakrishnan et al (2018) and Li and Li (2018).…”

Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Nadeb¹,

Torabi²,

Dolati³

2020

Mathematical Inequalities &Amp; Applications

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Let X λ1 , . . . , X λn be dependent non-negative random variables and Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi 's, with E[I pi ] = p i , i = 1, . . . , n. In actuarial sciences, Y i corresponds to the claim amount in a portfolio of risks.In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters λ 1 , . . . , λ n and p 1 , . . . , p n and the variables in the other set have the parameters λ

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“…The problem of stochastic comparisons of some quantities such as the number of claims, the aggregate claim amounts, the smallest and the largest claim amounts in two portfolios, have been considered by many researches in literature; see, e.g., Karlin and Novikoff (1963), Ma (2000), Frostig (2001), Hu and Ruan (2004), Denuit and Frostig (2006), Khaledi and Ahmadi (2008), Zhang and Zhao (2015), , Li and Li (2016), , Barmalzan et al (2016), Barmalzan et al (2017) and Balakrishnan et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model

Nadeb

Torabi

Dolati

2020

North American Actuarial Journal

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Let X λ1 , . . . , X λn be independent non-negative random variables belong to the transmuted-G model and let Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi 's, with E[I pi ] = p i , i = 1, . . . , n. In actuarial sciences, Y i corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters λ 1 , ..., λ n and the variables in the other set have the parameters λ * 1 , ..., λ * n . For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.

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Likelihood ratio and dispersive orders for smallest order statistics and smallest claim amounts from heterogeneous Weibull sample

Cited by 24 publications

References 5 publications

On fail‐safe systems under random shocks

On fail‐safe systems under random shocks

Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model

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