We present a new two parameter Burr XII distribution. The new density can be right skewed with no peak, unimodal-right skewed, left skewed and symmetric. The new failure rate can be decreasing, unimodal and increasing. Properties related to the new model are derived. Simple type copula-based construction is presented for deriving some new bivariate and multivariate type distributions. The maximum likelihood estimation, Anderson Darling estimation, right tail Anderson Darling estimation and left tail Anderson Darling estimation methods are used to estimate the model parameters. A new data set is analyzed for comparing estimations methods and the competitive models.

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived. Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

In this article, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index are performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "monotonically decreasing", "monotonically increasing", "increasing-constant", "upside-down-constant", "decreasing-constant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The applicability of the new life distribution is illustrated by means of two real data sets.

In our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains.