A Unified Approach to Ordering Comparison of GPS Distributions with their Mixtures

Jazi, Mansour Aghababaei; Alamatsaz, Mohammad Hossein; Abbasi, Somayyeh

doi:10.1080/03610926.2010.489177

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…Without any restriction on the tilt parameter θ, we have THEOREM 4. 4. The following orders are preserved by transformation from a baseline distribution to its corresponding Harris family and vice versa.…”

Section: Preservation Of Stochastic Orders By Harris Family With the Same Tilt Parametersmentioning

confidence: 99%

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Preservation properties of stochastic orders by transformation to Harris family

Abbasi¹,

Alamatsaz²

2018

pms

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Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.

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Section: Preservation Of Stochastic Orders By Harris Family With the Same Tilt Parametersmentioning

confidence: 99%

“…Nanda and Das [29] studied stochastic orders in the Marshall-Olkin family. Aghababaei and Alamatsaz [3], Aghababaei et al [4] and Alamatsaz and Abbasi [6] were concerned with stochastic comparisons of different distributions with their mixtures.…”

Section: Introductionmentioning

confidence: 99%

Preservation properties of stochastic orders by transformation to Harris family

Abbasi¹,

Alamatsaz²

2018

pms

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“…Modality and divisibility properties of these distributions are known in the literature. Stochastic ordering comparison between these distributions and their mixtures has also been recently of interest by Misra et al [1], Alamatsaz and Abbasi [2], Aghababaei Jazi and Alamatsaz [3], Abbasi et al [4] and Aghababaei Jazi et al [5].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Misclassified Generalized Power Series Distributions Under Different Loss Functions

Ahmad¹

2020

JSTA

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In certain experimental investigations involving discrete distributions external factors may induce measurement error in the form of misclassification. For instance, a situation may arise where certain values are erroneously reported; such a situation termed as modified or misclassified has been studied by many researchers. Cohen (J. Am. Stat. Assoc. 55 (1960), 139-143; Ann. Inst. Stat. Math. 9 (1960), 189-193; Technometrics. 2 (1960), 109-113) studied misclassification in Poisson and the binomial random variables. In this paper, we discuss misclassification in the most general class of discrete distributions, the generalized power series distributions (GPSDs), where some of the observations corresponding to x = c+1; c ≥ 0 are erroneously observed or at least reported as being x = c with probability 𝛼. This class includes among others the binomial, negative binomial, logarithmic series and Poisson distributions. We derive the Bayes estimators of functions of parameters of the misclassified GPSD under different loss functions. The results obtained for misclassified GPSD are then applied to its particular cases like negative binomial, logarithmic series and Poisson distributions. Finally, few numerical examples are provided to illustrate the results.

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“…Ghitany and Kotz (2007) investigated reliability properties of extended linear failure rate distributions using stochastic orderings. Stochastic comparison of different distributions with their mixtures were the concern of Alamatsaz and Abbasi (2008), Jazi and Alamatsaz (2010) and Jazi et al (2011). Huang and Da (2012) used stochastic orderings to compare members of Marshall-Olkin family.…”

Section: Introductionmentioning

confidence: 99%

Preservation properties of stochastic orderings by transformation to Harris family with different tilt parameters

Abbasi¹,

Alamatsaz²,

Cramer³

2016

ALEA

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Harris family of distributions models lifetime of a series system when the number of components is a positive random variable. In this paper, we reveal several stochastic comparisons in the Harris family with different tilt parameters and different baseline distributions with respect to the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stochastic orderings. Such comparisons are particularly useful in lifetime optimization of reliability systems. We shall also present two bounds for a Harris family survival function conditioned on its tilt parameter which are useful when aging properties are considered. Our results generalize several previous findings in this connection.

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A Unified Approach to Ordering Comparison of GPS Distributions with their Mixtures

Cited by 7 publications

References 8 publications

Preservation properties of stochastic orders by transformation to Harris family

Preservation properties of stochastic orders by transformation to Harris family

Bayesian Analysis of Misclassified Generalized Power Series Distributions Under Different Loss Functions

Preservation properties of stochastic orderings by transformation to Harris family with different tilt parameters

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