Relationship between the weighted distributions and some inequality measures

Behdani, Zahra; Borzadaran, Gholam Reza Mohtashami; Gildeh, Bahram Sadeghpour

doi:10.1080/03610926.2017.1397171

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…It is worth noting that the length-biased distribution and equilibrium distribution (as a weighted distribution) resemble the Lorenz curve quite closely. Now considering the relationship between the TTT transform and Lorenz curve as well as Propositions 5.9 and 5.14 of Behdani et al [7], provides helpful information regarding these relationships. For the length-biased distribution, we have the following expressions shown in Table 4 for some reliability measures and their relationships with the TTT transform, where…”

Section: Fr Functionmentioning

confidence: 99%

“…Let X and Y be two random variables, let F and G be their distribution functions, and let w i , i = 1, 2 be two monotone left continuous functions. Misra et al [33], Izadkhah et al [22], Izadkhah et al [23], and Behdani et al [7] obtained the criteria for preserving some stochastic orders under various assumptions. All of these findings lead to the conclusion that the TTT order has been formed as X w1 ≤ ttt Y w2 .…”

Section: Stochastic Ordering Of Weighted Distributionsmentioning

confidence: 99%

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Theoretical aspects of total time on test transform of weighted variables and applications

Esfahani¹,

Borzadaran²,

Amini³

2023

Kybernetika

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Although the total time on test (TTT ) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the behavior of the failure rate function of such variables based on the TTT transform. In addition, the conditions for establishing the T T T transform ordering for weight variables and its relationship with some stochastic orders have been investigated, and the conditions for establishing the TTT transform order as well as the presentation of the new better than used in total time on test transform (NBUT ) class of the weighted variables have also been studied. Finally, by analyzing the real data sets, applications of the transform introduced in the fit of a model is presented, and it is shown that weighted models have a significant advantage over the base models.Keywords: total time on test transform, generalized failure rate, generalized reversed failure rate, new better than used in total time on test transform, weight function

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Section: Fr Functionmentioning

confidence: 99%

Section: Stochastic Ordering Of Weighted Distributionsmentioning

confidence: 99%

Theoretical aspects of total time on test transform of weighted variables and applications

Esfahani¹,

Borzadaran²,

Amini³

2023

Kybernetika

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“…is decreasing and therefore, in accordance with (5), the random age after a shock is smaller than it was before in the sense of the likelihood ratio ordering, i.e., t lr t XX  . It should be also noted that, as follows from ( 19), this operation with the corresponding age compositions (densities) can be described in terms of the weighted distributions (Behdani et al, 2018).…”

Section: Populations Under Shocksmentioning

confidence: 99%

Improving the age composition of dynamic populations of manufactured items

Finkelstein

Hwan

2023

Statistics & Probability Letters

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Connection of Generalized Failure Rate and Generalized Reversed Failure Rate with Inequality Curves

Behdani

Borzadaran

Gildeh

2019

Int. J. Rel. Qual. Saf. Eng.

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The purpose of this paper is to introduce some properties of generalized failure rate (GFR) and generalized reversed failure rate (GRFR), study their connection with inequality measures and then apply it to make comparisons of some reliability models. In the second part of our paper, we obtain the properties for the GRFR based on the properties of the GFR and weighted distributions. The importance of such a study lies in the usefulness of using. Finally, we present two examples to illustrate the applications of the relationships outlined in this paper. A real dataset is used for clarifying presented concepts.

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Relationship between the weighted distributions and some inequality measures

Cited by 3 publications

References 24 publications

Theoretical aspects of total time on test transform of weighted variables and applications

Theoretical aspects of total time on test transform of weighted variables and applications

Improving the age composition of dynamic populations of manufactured items

Connection of Generalized Failure Rate and Generalized Reversed Failure Rate with Inequality Curves

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