Geometric visualization of parallel bivariate Pareto distribution surfaces

Abdel-All, Nassar H.; Abd-Ellah, H. N.

doi:10.1016/j.joems.2015.03.001

Cited by 1 publication

(1 citation statement)

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“…Recall that the Pareto distribution is often used to describe the allocation of wealth among individuals as in any society, a large portion of the wealth is in hands of a small percentage of people in that society. It is also useful in analyzing stock price fluctuations, studying the claim amounts in insurance companies and in comparing different systems [1,18]. Below, we discuss two such applications:…”

Section: Applicationsmentioning

confidence: 99%

Stochastic comparison of parallel systems with Pareto components

Naqvi¹,

Ding²,

Zhao³

2021

Prob. Eng. Inf. Sci.

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Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

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Section: Applicationsmentioning

confidence: 99%