In this article, a new cubic transmuted (CT) family of distributions has been proposed by adding one more parameter. We have introduced cubic transmuted uniform (CTU) distribution by using the proposed class. We have also provided a detail description of the statistical properties of the proposed CTU distribution along with its estimation and real-life application.

Transmutation is the functional composition of the cumulative distribution function (cdf) of one distribution with the inverse cumulative distribution function (quantile function) of another. Shaw and Buckley(2007), first apply this concept and introduced quadratic transmuted family of distributions. In this article, we have presented a review about the transmuted families of distributions. We have also listed the transmuted distributions, available in the literature along with some concluding remarks.

We have proposed a new multivariate Weibull distribution as a compound distribution of univariate Weibull distributions. We have studied some properties of the proposed distribution. The multivariate distribution of records for proposed distribution has also been studied. Estimation of the parameters has been done alongside application to the real data set.

The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joint and conditional and joint survival function moments and measures of dependence. The parameters of the proposed class of distributions are estimated using the maximum likelihood method of estimation. A multivariate version of the proposed class is also proposed, and some necessary properties are discussed. The multivariate dependence measures are obtained for the proposed multivariate class of distributions. A new bivariate power function distribution is proposed using the power function distribution as a baseline distribution in the proposed bivariate class. Some useful properties of the proposed bivariate distribution are studied. The parameters of the proposed bivariate distribution are estimated using the maximum likelihood method. An extensive simulation study has been conducted to see the performance of the estimation method. The new bivariate power function distribution is used to model some real data.

The cubic transformation families of distributions are widely used to model complex univariate data. However, in many situations, the jointly modeling of two variables is necessary, making bivariate distributions essential. This paper introduces a novel family of bivariate probability distributions that extends the univariate cubic transformation family. The bivariate cubic transmuted (BCT) family of distributions is comprehensively discussed, with its statistical properties explored in detail. Within this family, the bivariate cubic transmuted Burr (BCTB) distribution is specifically analyzed. Its statistical properties are examined, and its parameters are estimated using the maximum likelihood estimation (MLE) method. To assess the performance of the estimation procedure, a Monte Carlo simulation study is conducted. Furthermore, the applicability of the proposed model is demonstrated by fitting it to real datasets, and its relevance is further discussed.