On the exact distribution of generalized Hollander-Proschan type statistics

Ghosh, Shyamal; Mitra, Manimala

doi:10.1080/03610918.2020.1753076

Cited by 1 publication

(1 citation statement)

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“…Our objective is to provide an overview of these advancements. Researchers in statistics and reliability analysis have looked at testing exponentiality problems using different age classes of life distributions from a variety of angles; for more information, see Bryson and Siddiqui [1], Bhattacharyya et al [2], Barlow and Proschan [3], Klefsjo [4], Khan et al [5], Kumazawa [6], Mahmoud et al [7,8], Majumder and Mitra [9], Bhattacharyya et al [10], Navarro [11], Abu-Youssef et al [12], Ghosh and Mitra [13], Navarro and Pellerey [14], El-Morshedy et al [15], EL-Sagheer et al [16] Gadallah et al [17], Mansour [18], Ghosh and Mitra [19], Majumder and Mitra [20], Lai and Xie [21], Etman et al [22], Ghosh and Majumder [23], Bakr and Al-Babtain [24], and Ghosh and Mitra [25] and Alqifar et al [26]. The goodness-of-fit test indicates whether the data in one's sample correspond to the data one would anticipate seeing in the actual population.…”

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confidence: 99%

The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data

et al. 2023

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The majority of approaches proposed in the past few decades to solve life test problems have differed markedly from those used for closely related, yet broader, issues. Due to the complexity of data that are generated each day in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability has been created. This domain is referred to as life classes, where specific probability distributions are presented. In this study, it is shown that the use of the quality-of-fit technique to solve problems involving life testing makes sense, and produces simpler processes that are roughly equivalent or superior to those used in traditional procedures. They may also behave better in limited samples. This work investigates a novel quality-of-fit test statistic; it is based on an exponential transform and is compared to the best renewal used Laplace test in increasing convex ordering (NBRULC). Evidence for approach normality is provided. The calculated variables include powers, Pitman asymptotic effectiveness, and critical points. Methods on how to handle censored data were also studied. Our experiments have real-world applications in the fields of medicine and engineering.

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