In this work, we propose a new three parameter distribution called the Burr XII inverse Rayleigh model, this model is a generalization of the inverse Rayleigh distribution using the Burr XII family introduced by Cordeiro et al. [The burr XII system of densities: properties, regression model and applications. J. Stat. Comput. Simul. 88 (2018), pp. 432–456]. After studying the statistical characterization of this model, we construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic in the presence of two cases: censored and complete data. We describe the theory and the mechanism of the $Y_n^2$ statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on initial non grouped data. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.

In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose.

In this paper, we introduce a new extension of the Inverse Weibull distribution along with a number of its mathematical properties. Next, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic for censored and complete data. We describe the theory and the mechanism of the \(Y_{n}^{2}\) test statistic which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.

In this paper, we Örst introduse a new extension of the exponentiated exponential distribution along with its several mathematical properties. Second, we construct a modiÖed Chi-squared goodness-of-Öt test based on the Nikulin-Rao-Robson statistic in presence of censored and complete data. We describe the theory and the mechanism of the Y 2 n statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various Öelds, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other right censored data sets.