Preservation of classes of life distributions under weighting with a general weight function

Abstract

To cite this version:Pawel Blażej. Preservation of classes of life distributions under weighting with a general weight function. Statistics and Probability Letters, Elsevier, 2010, 78 (17)

On a New Class of Multivariate Prior Distributions: Theory and Application in Reliability

“…This result extends the property (1.10) from the case n = 1 to n ≥ 2. Moreover, for n = 1 this result plays an equivalent role to Lemma 1 in Arias-Nicolás et al (2016) and Theorem 1 of Blazej (2008). Now, let us suppose that the decision-maker is able to represent the changes in a prior belief, π, by a decreasing weight function, w 1 , and an increasing weight function, w 2 .…”

“…where the weight function ω(θ) = h [F π (θ)] depends on F π (this is noted, for example, in Furman and Zitikis (2008) and Blazej (2008)). In other words, when we consider absolutely continuous random variables, weighted distributions are more general objects than distorted distributions.…”

On preservation under univariate weighted distributions

“…Numerous research works have also been devoted to investigate the properties of weighted distributions in the context of stochastic orderings and aging classes (cf. Bartoszewicz and Skolimowska [4], Misra et al [11], B lażej [5], Bartoszewicz [3] and Izadkhah et al [7]). One of the main problems in some of these works was the problem of preservation of stochastic orders and aging classes under univariate weighted distributions.…”

“…One of the main problems in some of these works was the problem of preservation of stochastic orders and aging classes under univariate weighted distributions. For example, using a representation of weighted distributions B lażej [5] and Bartoszewicz [3] obtained some results for preservation of several stochastic orders and aging classes. By appealing to some bivariate characterizations of stochastic orders Misra et al [11] derived a similar kind of results.…”

Stochastic Properties of the Weighted Hazard Rate Order

“…For some recent works in applied probability we refer the readers to Unnikrishnan and Sunoj [21], Navarro et al [16], Alavi and Chinipardaz [1], Li et al [12] and Izadkhah et al [7]; and for some recent works in applied statistics we refer the readers to Cutillo et al [5], Feizjavadian and Hashemi [6] and Karimi and Alavi [9] among others. In particular, reliability analysis of the weighted distributions has received much attention in the literature in the recent past decades (see, for instances, Nanda and Jain [15], Navarro et al [17], Bartoszewicz and Skolimowska [3], Błazej [4] and Kayid et al [11]). In reliability and survival analysis, when data are unknowingly sampled from a weighted distribution as opposed to the parent distribution, the survival function, the hazard rate function, and the mean residual life function may be underestimated or overestimated depending on the form of the weight function.…”