Nonparametric Testing for Unknown Age (UBAL) Class of Life Distribution

Abstract

In this article, a test statistic for testing exponentiality versus a used better than aged in Laplace transform ordering class of life distribution based on a U-statistic is proposed. Pitman’s asymptotic efficiencies of the test are calculated and compared to other tests. The percentiles of this test statistic are tabulated for censored and non-censored data, and the powers of this test are estimated for some famously alternative distributions in reliability, such as the Weibull, Makeham, linear failure rate, and Gamma distributions. Finally, examples in different areas are used as practical applications of the proposed test.

Statistical Modeling of Some Cancerous Diseases Using the Laplace Transform Approach of Basic Life Testing Issues

“…In addition, the percentage points of the proposed statistics are simulated. The efficacies of our developed tests are compared to El-Arishy et al [ 17 ] and Abu-Youssef et al [ 14 ] based on Pitman asymptotic relative efficiency using some well-known life distributions, namely, linear failure rate family (LFR) and Weibull family. Finally, the findings of the paper are applied to some medical real datasets.…”

“…Here, we create a test statistic to test if H 0 : F is exponential, against H 1 : F is UBA mgf . Nonparametric testing for classes of life distributions has been considered by many authors (see Abu-Youssef et al [ 16 , 18 ] and Mahmoud et al [ 19 ].…”

“…Properties and applications of these aging notions can be found, Navarro and Pellerey [ 1 ], Bryson and Siddiqui [ 2 ], Barlow and Proschan [ 3 ], Abu-Youssef and Bakr [ 4 ], Mahmoud et al [ 5 ], EL-Sagheer et al [ 6 ], Esary et al [ 7 ], Navarro J. [ 8 ], Cao and Wang [ 9 ], Fernandez-Ponce et al [ 10 ], Ali [ 11 ], Hassan and Said [ 12 ], Ahmad [ 13 ], Qureshi et al [ 14 ], Yusuf and Qureshi [ 15 ], and Abu Youssef et al [ 16 , 17 ] investigated the moment generating function for UBA (UBA mgf ).…”

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

“…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.…”

Modeling Various Survival Distributions using a Nonparametric Hypothesis Testing Based on Laplace Transform Approach with Some Real Applications

“…Barlow and Proschan [ 7 ], Abu-Youssef and Bakr [ 8 ], Abu-Youssef et al [ 9 ], Franco et al [ 10 ], Deshpande et al [ 11 ], Hu and Xie [ 12 ], Qureshi and Yusuf [ 13 ], Hassan and Said [ 14 ], Sania Qureshi and Rashid Jan [ 15 ], Abu-Youssef et al [ 16 , 17 ], and Lia and Xie [ 18 ], and others proposed the probabilistic features of the aging distributions in the literature. The following are the relationships between the previous classes: …”