Some weighted distribution results on univariate and bivariate cases

Stochastic Properties of the Weighted Hazard Rate Order

“…It is directly seen from Theorem 3.1 that if we take w as a constant function and v as an increasing function and also if we take v as a constant function and w as a decreasing function, then we derive the following corollary. Note that the result of Corollary 3.1 is known in the literature (see for instances Theorem 2.1 of Nanda and Jain [15], Theorem 9(a) of Bartoszewicz and Skolimowska [3] and Theorem 3.2(b) of Misra et al [14]). …”

“…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.…”

On preservation under univariate weighted distributions

“…Recently, the study of some reliability aspects of weighted distributions has attracted the attention of many researchers (cf. Kochar and Gupta [10], Nanda and Jain [12], Navarro et al [14] and Pakes et al [15] among others). Numerous research works have also been devoted to investigate the properties of weighted distributions in the context of stochastic orderings and aging classes (cf.…”

A New Class of Generalized Modified Weibull Distribution with Applications

“…(Rao 1965) unified concept of weighted distribution and use it to identify various sampling situations. The usefulness and applications of weighted distribution to biased samples in various areas including medicine, ecology, reliability, and branching processes can also be seen in (Nanda and Jain 1999), (Gupta and Keating 1985), (Oluyede 1999) and in references therein. Let Y be a non-negative random variable with its natural pdf f (y; θ), where θ is a vector of parameters, then the pdf of the weighted random variable Y w is given by:…”