A Proportional Hazard Marshall–Olkin Extended Family of Distributions and its Application to Gompertz Distribution

Al-Jarallah, R. A.; Ghitany, M. E.; Gupta, Ramesh C.

doi:10.1080/03610926.2012.715226

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…Recently Batsidis and Lemonte (2015) discussed several results in connection with behavior of the failure rate function for Harris family and discussed certain related stochastic orderings. Al-Jarallah et al (2014) presented a proportional hazard version of Marshall-Olkin family of distribution as [H(. ; θ, 1)] γ and investigated likelihood ratio ordering in this model.…”

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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Section: Introductionmentioning

confidence: 99%

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

Abbasi¹,

Alamatsaz²,

Cramer³

2016

ALEA

View full text Add to dashboard Cite

show abstract

“…For a better understanding of this point, we refer the interested reader to Marshall and Olkin works. Marshall-Olkin Extended (MOE) distribution, introduced by Al-Jarallah et al [1] has pd f (probability density function) and cd f (cumulative distribution function) given respectively by…”

Section: Introductionmentioning

confidence: 99%