Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

EL‐Sagheer, Rashad M.; Mahmoud, M. A. W.; Etman, Walid B. H.

doi:10.17713/ajs.v47i1.579

Cited by 10 publications

(5 citation statements)

References 14 publications

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“…Increasing failure rate (IFR), New better than used (NBU), Used better than age (UBA), and EBU are the most popular of these classes, Navarro and Pellerey, 1 Barlow and Proschan, 2 Bryson and Siddiqui, 3 Navarro, 4 and Esary et al 5 Other aging categories, such as Laplace ordering, and the order of moment generating function for these categories have been considered by many researchers. Fernandez-Ponce et al, 6 Ahmad, 7 Abu Youssef et al, 8 Etman et al, 9 EL-Sagheer et al, 10 Abu-Youssef et al, 11 Bakr et al, 12 EL-Sagheer et al, 13 Mahmoud et al 14 and Gadallah et al 15 The fundamental needs of contemporary science and technology compelled the development of a systematic approach for the investigation of any event or activity taking place in the world. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products.…”

Section: Introductionmentioning

confidence: 99%

“…Other aging categories, such as Laplace ordering, and the order of moment generating function for these categories have been considered by many researchers. Fernandez‐Ponce et al., 6 Ahmad, 7 Abu Youssef et al., 8 Etman et al., 9 EL‐Sagheer et al., 10 Abu‐Youssef et al., 11 Bakr et al., 12 EL‐Sagheer et al., 13 Mahmoud et al 14 . and Gadallah et al 15 …”

Section: Introductionmentioning

confidence: 99%

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On basic life testing issues in medical research using non‐parametric hypothesis testing

Bakr

2023

Quality & Reliability Eng

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The probability life distributions usually describe the time to event or survival time. Therefore, these life distributions play a crucial role in the analysis and projection of the maximum life expectancy using the Laplace transform technique for nonparametric hypothesis testing. A flexible framework for monitoring randomized clinical trials utilizing prior knowledge of certain phenomena under uncertainty is provided by the Laplace transform. By considering the previous data, medical professionals can also utilize these estimators to calculate the chance of tumor recurrence, cardiovascular death, and AIDS for HIV patients. However, censoring occurs in clinical trials and medical studies when the precise event's time of occurrence is unknown. The present study aims to propose a new test for exponential better than used (EBU). The suggested statistical test's efficiency and critical values are computed and compared with those of previous classes. Furthermore, the suggested test statistic is provided in bivariate form as well. Finally, the methodology is then tested using medical data in order to provide evidence that it is applied efficiently.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On basic life testing issues in medical research using non‐parametric hypothesis testing

Bakr

2023

Quality & Reliability Eng

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“…The most well-known classes proposed over the past few decades include increasing failure rate and average (IFR and IFRA), new better than used and expectation (NBU and NBUE), used is better than aged (UBA), and used better than aged in moment generating function (UBAmgf). One might consult Deshpand et al [1], Klefsjo [2], Ahmed [3,4], Bakr et al [5], Barlow and Proschan [6], Rolski [7], Abu Youssef et al [8], Etman et al [9], EL-Sagheer et al [10], Abu Youssef et al [11], Bakr et al [12], EL-Sagheer et al [13], Mahmoud et al [14], Gadallah et al [15], and Bakr and Al Babtain [16].…”

Section: Introductionmentioning

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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Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

Cited by 10 publications

References 14 publications

On basic life testing issues in medical research using non‐parametric hypothesis testing

On basic life testing issues in medical research using non‐parametric hypothesis testing

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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