Nonparametric Test for a class of Lifetime Distribution UBAC(2) Based on the Laplace Transform

Abstract

Testing various classes of life distributions have been considered a very important problem in the literature during the last decades, and many authors tried to solve it. In this paper, a new statistic technique for testing exponentiality versus the class of life distribution used better than aged in increasing concave ordering (UBAC(2)) is introduced based on the Laplace transform. For this proposed test, the critical values, the pitman’s asymptotic efficiency and the power of the test are calculated via simulation to assess the performance of the test. A new nonparametric test statistic for testing exponentiality versus UBAC(2) for right censored data is proposed, and the critical values are tabulated. Finally, real data are used for complete and censored data by using our proposed test.

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

“…Many researchers use non-parametric tests to assess data exponentiality against many classes of life distributions using various techniques, for example, Abu-Youssef and El-Toony [20], Mahmoud et al, [21], Etman et al, [22], Ghosh and Mitra [23], Navarro [24], and Belzunce [25], among others. Now, we develop an exponential departure measure towards the NBRUmgf class.…”

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

“…Suppose that the following random sample 𝑋 1 , 𝑋 2 , … , 𝑋 𝑛 was taken from 𝐹 to apply this non-parametric testing. Several authors have introduced non-parametric hypothesis testing for a variety of life distributions (Bakr et al, 17 Mansour, 18 Abu-Youssef and El-Toony, 19 EL-Sagheer et al 20 and Mahmoud et al 21 From (1.1), The measure of departure can be written as: (assume that 𝜇 is equal one):…”