Mean Inactivity Time Function, Associated Orderings, and Classes of Life Distributions

In this paper, we introduce a new distribution generated by an integral transform of the probability density function of the weighted exponential distribution. This distribution is called the weighted exponential-Gompertz (WE-G). Its hazard rate function can be increasing and bathtubshaped. Several statistical properties of the new model are obtained, such as moment generating function, moments, conditional moments, mean inactivity time, mean residual lifetime and Rényi entropy. The maximum likelihood estimation of unknown parameters is introduced. A real data application demonstrates the performance of the new model.

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“…From Equation (11) and expanding the term [1 − exp(−σ (e λx − 1)) ] β (i α+1) , the cdf of WE-G can be rewritten as 1) .…”

Section: Expansion For the Cdfmentioning

confidence: 99%

On weighted exponential-Gompertz distribution: properties and application

El-Bar

Ragab

2019

Journal of Taibah University for Science

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“…Then 8) and the equality holds if and only if X follows the distribution having cumulative distribution function…”

Section: Theorem 24 Let X Be An Absolutely Continuous Random Variablmentioning

confidence: 99%

“…They are closely related in the sense that both of them determine a distribution uniquely via the relation and Kayid and Izadkhah (2014). In analogy with Jiang et al (2003), the reversed AI function of X is defined as follows.…”

Section: Introductionmentioning

confidence: 99%

Inequalities involving expectations of selected functions in reliability theory to characterize distributions

Kundu

Ghosh

2017

Communications in Statistics - Theory and Methods

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Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some wellknown distributions. However, there has been growing interest in the study of these functions in reversed time and their applications. In the present work we consider reversed hazard rate, expected inactivity time and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.

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“…Shock models of this kind, called Poisson shock models, have been studied extensively. Some recent references are Izadkhah and Kayid (2013), Kayid et al (2013) and Kayid and Izadkhah (2014), among others. Firstly, let us define the discrete version of the DLTTF class.…”

Section: Theorem 41 If the Lifetime Random Variable X Is Ifra Thenmentioning

confidence: 99%

Laplace transform ordering of time to failure in age replacement models

Kayid

Izadkhah

Alshami

2016

Journal of the Korean Statistical Society

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a b s t r a c tThe concept of mean time to failure in age replacement models plays an important role in reliability and life testing. In this paper, based on the comparison of Laplace transform of time to failure in an age replacement model, we introduce and study a new stochastic order. This new order is stronger than the Laplace transform and the mean time to failure in the age replacement model orders. Some motivations and descriptions of the proposed stochastic order are provided. In addition, several characterizations and preservation properties of the new order under some well-known reliability operations are discussed. As a consequence, a new class of life distributions is proposed, and some of its reliability properties are investigated. Finally, the problem of testing exponentiality against such class is discussed and some numerical results are presented.

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Mean Inactivity Time Function, Associated Orderings, and Classes of Life Distributions

Cited by 56 publications

References 23 publications

On weighted exponential-Gompertz distribution: properties and application

On weighted exponential-Gompertz distribution: properties and application

Inequalities involving expectations of selected functions in reliability theory to characterize distributions

Laplace transform ordering of time to failure in age replacement models

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