In this article, a new three parameter lifetime model is proposed as a generalisation of the moment exponential distribution. The proposed model is named as Topp-Leone moment exponential distribution. The induction of two additional shape parameters will enhance the capability of the proposed model to handle the complex scenarios in modelling. Several properties of the proposed model are discussed. The model parameters are estimated using method of maximum likelihood. Real life applications of the proposed model have been carried out by using datasets from the fi elds of botany, archaeology and ecology.

Dual generalized order statistics is a unified method for random variables that are arranged in decreasing order. The moments of dual generalized order statistics are helpful to study the properties of any distribution. Often, the moments of dual generalized order statistics are not easy to compute and recursive computation is done. The recurrence relations for moments of generalized and dual generalized order statistics are helpful to compute the higher order moments from the lower order moments. In this paper the methods for recursive computation of moments of dual generalized order statistics for general transmuted power function distributions are presented. The general transmuted power function distributions are first defined and then the recurrence relations are obtained. These recurrence relations include relations for single, inverse, product, and ratio moments. The recurrence relations are used to obtain the relations for moments of special cases, which include lower record values and reversed order statistics. Some characterizations of the general transmuted power function distributions are also presented based on the basis of single and product moments of dual generalized order statistics. These characterizations are unique results for the general transmuted power function distributions. The results given in the paper are useful to obtain the results for special cases of general transmuted power function distribution which includes power function and transmuted power function distributions.

Multivariate distributions are helpful in the simultaneous modeling of several dependent random variables. The development of a unique multivariate distribution has been a difficult task and different multivariate versions of the same distribution are available. The need is, therefore, to suggest a method of obtaining a multivariate distribution from the univariate marginals. In this paper, we have proposed a new method of generating the multivariate families of distributions when information on univariate marginals is available. Specifically, we have proposed a multivariate family of distributions which provides a univariate transmuted family of distributions as marginal. The proposed family is a re-parameterization of the Cambanis (1977) family. Some properties of the proposed family of distributions have been studied. These properties include marginal and joint marginal distributions, conditional distributions, and marginal and conditional moments. We have also obtained the dependence measures alongside the maximum likelihood estimation of the parameters. The proposed multivariate family of distributions is studied for the Weibull baseline distributions giving rise to the multivariate transmuted Weibull (MTW) distribution. Real data application of the proposed MTW distribution is given in the context of modeling the daily COVID-19 cases of the World. It is observed that the proposed MTW distribution is a suitable fit for the joint modeling of the COVID-19 data.