Preservation properties of stochastic orderings bytransformation to Harris family with different tiltparameters
TLDR
In this paper, the authors reveal several stochastic comparisons in the Harris family with different tilt parameters and different baseline distributions with respect to the usual baseline distributions, i.e., the shift-stochastic, shift-proportional, proportional, and shifted proportional orderings.Abstract:
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.read more
Citations
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Journal ArticleDOI
Preservation properties of stochastic orders by transformation to Harris family
TL;DR: In this paper, using Harris family distributions, the authors compared the lifetimes of two series systems with random number of components, with respect to several types of stochastic orders.
Journal ArticleDOI
Preservation properties of stochastic orders by transformation to the transmuted-G model
Hossein Nadeb,Hamzeh Torabi +1 more
TL;DR: In this article, the authors consider stochastic comparisons in the transmuted-G family with different parametrized distributions, and show that the transmutation-G model is a useful technique to construct some new distributions by adding a parameter.
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Orderings of fail-safe systems with components having Marshall-Olkin-Harris lifetime distributions
TL;DR: In this article , the authors discuss stochastic comparisons of two fail-safe systems in two different directions and present sufficient conditions for the usual stochastically order between two fail safe systems with different lifetime distributions but with the same Archimedean copula for their joint distribution.
Journal ArticleDOI
Some bounds related to Harris family of distributions
TL;DR: As a lifetime distribution, Harris family of distributions are applied to the lifetime of a series system with random number of components in this paper, where the properties of various ageing classes of mi....
References
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Statistical Theory of Reliability and Life Testing Probability Models
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Albert W. Marshall,Ingram Olkin +1 more
TL;DR: In this article, a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used twoparameter families of life distributions as the Weibull, gamma and lognormal distributions.
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A Function for Size Distribution of Incomes
S. K. Singh,G. S. Maddala +1 more
TL;DR: In this article, the authors derived a distribution that is a generalization of the Pareto distribution and the Weibull distribution used in analyses of equipment failures, and the distribution fits actual data remarkably well compared with the pareto and the lognormal.
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A Note on Probability Distributions with Increasing Generalized Failure Rates
TL;DR: This work provides alternative characterizations of the IGFR property that lead to simplify verifying whether the IG FR condition holds and relates the limit of the generalized failure rate and the moments of a distribution.