A new family of distributions called the Kumaraswamy Rayleigh family is defied and studied. Some of its relevant statistical properties are derived. Many new bivariate type G families using the of Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. The method of the maximum likelihood estimation is used. Some special models based on log-logistic, exponential, Weibull, Rayleigh, Pareto type II and Burr type X, Lindley distributions are presented and studied. Three dimensional skewness and kurtosis plots are presented. A graphical assessment is performed. Two real life applications to illustrate the flexibility, potentiality and importance of the new family is proposed.

A new compound generalization of the Lomax lifetime model is presented and studied. The novel model is established based on the Poisson Topp-Leone family of Merovci et al. (2020). The novel density can be “right skewedwith heavy tail”, “symmetric” and “left skewedwith heavy tail”. The corresponding failure rate can be “monotonically decreasing”, “increasingconstant”, “upside down”, “upside down-constant” and “reversed J-shape”. Relevant characteristics are derived and discussed. numerical and graphical analysis for some statistical properties are presented. we derived some new bivariate extensions via some common copulas. Graphical assessment for the maximum likelihood estimation is presented. Graphical assessment for the maximum likelihood estimation is presented. Two real-life data sets are analyzed and modelled using the novel model. The new model proven its superiority against fourteen competitive Lomax extensions.

In this work, we introduce a new G family with two-parameter called the compound reversed Rayleigh-G family. Several relevant mathematical and statistical properties are derived and analyzed. The new density can be heavy tail and right skewed with one peak, symmetric density, simple right skewed density with one peak, asymmetric right skewed with one peak and a heavy tail and right skewed with no peak. The new hazard function can be "upsidedown-constant", "constant", "increasing-constant", "revised J shape", "upside-down", "J shape" and "increasing". Many bivariate types have been also derived via di¤erent common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and ‡exibility of the new family is illustrated by means of two real data sets.

In this paper, we introduce a new continuous log-logistic extension. Several of its properties are established. A numerical analysis for skewness and kurtosis is presented. The new failure rate can be "bathtub or U shaped", "increasing", "decreasing-constant", "J shaped", "constant" and "decreasing". Many bivariate and Multivariate type distributions are derived using the Clayton Copula and the Morgenstern family. To assess of the finite sample behavior of the estimators, we performed a graphical simulation. Some useful applications are considered for supporting the new model.

In this study, a new Burr XII distribution is defined and studied. Various structural mathematical properties of the proposed model are investigated. The maximum likelihood method is used to estimate the model parameters. We assess the performance of the MLEs of the new distribution with respect to sample size n. The assessment was based on a simulation study. The new distribution is applied for modeling two real data sets to prove empirically its flexibility. The new Burr XII model can be viewed as a suitable model for fitting the right skewed and unimodal data. The new model provides adequate fits as compared to other Burr XII models by means of two applications.