A wide review on exponentiality tests and two competitive proposals with application on reliability. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Torabi, Hamzeh; Montazeri, Narges H.; Grané, Aurea
• Is Part Of: Journal of statistical computation and simulation. Volume 88:Issue 1(2018)
• Page Start: 108
• Page End: 139
• Publication Date: 2018-01-02
• Subjects: Empirical distribution function -- entropy estimator -- exponentiality test -- goodness-of-fit tests -- Monte Carlo simulation; 62F03 -- 62F10; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1379522
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In this paper, two new statistics based on comparison of the theoretical and empirical distribution functions are proposed to test exponentiality. Critical values are determined by means of Monte Carlo simulations for various sample sizes and different significance levels. Through an extensive simulation study, 50 selected exponentiality tests are studied for a wide collection of alternative distributions. From the empirical power study, it is concluded that, firstly, one of our proposals is preferable for IFR (increasing failure rate) and UFR (unimodal failure rate) alternatives, whereas the other one is preferable for DFR (decreasing failure rate) and BFR (bathtub failure rate) alternatives and, secondly, the new tests can be considered serious and powerful competitors to other existing proposals, since they have the same (or higher) level of performance than the best tests in the statistical literature.