GOODNESS-OF-FIT TESTS FOR THE NEW WEIBULL-G FAMILY OF DISTRIBUTIONS

Abstract

In this paper, we present two New models named New-Weibull-Weibull ($NWW$) and New-Weibull-Rayleigh ($NWR$) from The New-Wei- bull-G family recently introduced that can have a variety of hazard rate shapes that allows to describe observations from different fields of study. The unknown parameters of the $NWW$ and $NWR$ models have been estimated under the maximum likelihood estimation method. Moreover, we construct a modified chi-squared goodness-of-fit test based on the \textit{Nikulin– Rao–Robson} ($NRR$) statistic to verify the applicability of the proposed $NWW$ and $NWR$ models. The modified test shows that the models studied can be used as a good candidate for analyzing a large variety of real phenomena. The $NWW$ and $NWR$ models are applied upon a five different real complete and right-censored data sets in order to evaluate its practicability and flexibility.