A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data

El-Morshedy, Mahmoud; Al‐Bossly, Afrah; EL‐Sagheer, Rashad M.; Almohaimeed, Bader; Etman, Waleed B. H.; Eliwa, Mohamed S.

doi:10.3390/sym14112353

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Be aware that F 1 (u) and F 3 (u) reduce to exponential distributions for θ = 0, while F 2 (u) reduces to an exponential distribution for θ = 1. The PAE is defined by It is noted that the other tests that were studied in [28][29][30] do not depend on t • , while our proposed test depends on t • and, therefore, gave better results compared to the results mentioned in Table 1.…”

Section: Pitman's Asymptotic Efficiency Of ∆(M T • )mentioning

confidence: 84%

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

Alqifari

Eliwa

Etman

et al. 2023

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Due to the complexity of the data being generated day in and day out 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 called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t∘. Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman’s asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis.

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Section: Pitman's Asymptotic Efficiency Of ∆(M T • )mentioning

confidence: 84%

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

Alqifari

Eliwa

Etman

et al. 2023

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“…Testing exponentiality concerns against several types of aging class life distributions have been explored by statisticians and reliability analysts from diverse perspectives; for example, see Mahmoud et al [23], Navarro and Pellerey [24], Mahmoud El-Morshedy [25], and Navarro [26], among others. Several authors, including Mahmoud and Abdul Alim [27], Abu-Youssef and Gerges [28], and Abu-Youssef and El-Toony [29] have examined testing exponentiality using the goodness of fit approach.…”

Section: Definitionmentioning

confidence: 99%

Statistical Modeling for Some Real Applications in Reliability Analysis Using Non-Parametric Hypothesis Testing

Bakr

2023

Symmetry

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Probability life distributions usually describe the time to an event or survival time. Therefore, these life distributions play a crucial role in the analysis and projection of maximum life expectancy using the goodness of fit approach for nonparametric hypothesis testing. This study suggests a nonparametric technique to determine whether the data follow an exponential distribution or belong to the mathematical class of the moment generating function for used better than aged (UBAmgf). These tests can be applied to both censored and non-censored data. The upper percentile points of the test statistics are generated, and the suggested test’s asymptotic normality is established. Some well-known alternative asymmetric probability models are used to compute the Pitman asymptotic relative efficiency (PARE) and powers of the proposed test. To demonstrate the paper’s conclusions, some asymmetric real-world datasets are examined.

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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.…”

Section: Introductionmentioning

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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A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data

Cited by 5 publications

References 19 publications

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

Statistical Modeling for Some Real Applications in Reliability Analysis Using Non-Parametric Hypothesis Testing

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

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