A General Transmuted Family of Distributions

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.

Generating new statistical models is one of the most commonly used methods to represent real-life occurrences. Sometimes, with a known distribution, it may not be possible to represent a scenario, so we may consider generalization to incorporate more variance in the data. In this article, we offer a modified cubic transmuted-G family of distributions to enrich the members of the second-order transmuted distributions. By utilizing this modified class of distributions, we build a new distribution entitled the modified cubic transmuted Rayleigh distribution, along with its distributional features, estimate, associated inference, and real-life applications.