Résumé: In this paper, a new family of lifetime distributions called new two-parameter distribution-G family is introduced. This family includes some new distributions such as new two-parameter distribution -generalized linear exponential family. Some statistical properties of the proposed distribution are obtained, such as the hazard rate function, moments, moment generating function and order statistics. We discuss the estimation of the distribution parameters by method of maximum likelihood in both of complete and right censored cases. A modified criteria test is developed to fit this new model when the parameters are unknown and data are right censored. The performances of the methods used are demonstrated by an intensive simulation study whether the usefulness and the versatility in practical applications of this distribution is illustrated by means of real data sets.

Résumé: 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.

Résumé: Al-Shomrani et al. (2016) introduced a new family of distributions (TL-G) based on the Topp-Leone distribution (TL) by replacing the variable x by any cumulative distribution function G(t). With only one extra parameter which controls the skewness, this family is a good competitor to several generalized distributions used in statistical analysis. In this work, we consider the extended exponential as the baseline distribution G to obtain a new model called the Topp-Leone extended exponential distribution TL-EE. After studying mathematical and statistical properties of this model, we propose different estimation methods such as maximum likelihood estimation, method of ordinary and weighted least squares, method of percentile, method of maximum product of spacing, method of Cramer Von-Mises, modified least squares estimators and chi-square minimum method for estimating the unknown parameters. In addition to the classical criteria for model selection, we develop for this distribution a goodness-of-fit statistic test based on a modification of Pearson statistic. The performances of the methods used are demonstrated by an extensive simulation study. With applications to covid-19 data and waiting times for bank service, a comparison evaluation shows that the proposed model describes data better than several competing distributions.

Résumé: A new six-parameter continuous distribution called the Generalized Kuma-raswamy Generalized Power Gompertz (GKGPG) distribution is proposed inthis study, a graphical illustration of the probability density function andcumulative distribution function is presented. The statistical features of theGeneralized Kumaraswamy Generalized Power Gompertz distribution aresystematically derived and adequately studied. The estimation of the modelparameters in the absence of censoring and under-right censoring is perfor-med using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix ˆW ,ˆC , and ˆG , criteria test 2nY , alongside the quadratic form of the test statisticis derived. Mean simulated values of maximum likelihood estimates ˆγ andtheir corresponding square mean errors are presented and confirmed to agreeclosely with the true parameter values. Simulated levels of significance for( )2nY γ test for the GKGPG model against their theoretical values were rec-orded. We conclude that the null hypothesis for which simulated samples arefitted by GKGPG distribution is widely validated for the different levels ofsignificance considered. From the summary of the results of the strength of aspecific type of braided cord dataset on the GKGPG model, it is observedthat the proposed GKGPG model fits the data set for a significance level ε =0.05

Résumé: In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets.

Résumé: In this article, we propose the construction of modified chi-squared goodness-of-fit tests for the generalized Rayleigh distribution for both complete and censored data. These tests are based on the Nikulin–Rao–Robson (NRR) statistic and its modification proposed for right-censored data by Bagdonavičius and Nikulin. Numerical examples of simulated samples and real data are given to illustrate the usefulness of the proposed tests.