In this paper, a new family of distributions called exponentiated T -X distribution is defined. Some of its properties and special cases are discussed. A member of the family, namely, the three-parameter exponentiated Weibullexponential distribution is defined and studied. Some of its properties including distribution shapes, limit behavior, hazard function, Shannon entropy, moments, skewness and kurtosis are discussed. The flexibility of the exponentiated Weibull-exponential distribution is assessed by applying it to three real data sets and comparing it with other distributions. The exponentiated Weibull-exponential distribution is found to adequately fit left-skewed and right-skewed data sets.

In this paper, we propose new families of generalized Lomax distributions named T-LomaxfYg. Using the methodology of the Transformed-Transformer, known as T-X framework, the T-Lomax families introduced are arising from the quantile functions of exponential, Weibull, log-logistic, logistic, Cauchy and extreme value distributions. Various structural properties of the new families are derived including moments, modes and Shannon entropies. Several new generalized Lomax distributions are studied. The shapes of these T-LomaxfYg distributions are very flexible and can be symmetric, skewed to the right, skewed to the left, or bimodal. The method of maximum likelihood is proposed for estimating the distributions parameters and a simulation study is carried out to assess its performance. Four applications of real data sets are used to demonstrate the flexibility of T-LomaxfYg family of distributions in fitting unimodal and bimodal data sets from di erent disciplines.

The Lomax distribution, known as Pareto (type II) distribution, is a heavy tail probability distribution used extensively in business, economics and in actuarial modeling. The Weibull-Pareto distribution defined by Alzaatreh et al. (2013a) has shown high bias and standard error for the ML estimates when the parameter $c>>1$. In this paper we use the Lomax distribution to construct the Weibull-Lomax distribution. It is observed that the Weibull-Lomax distribution performs significantly better in terms of the ML estimations. Some structural properties of the Weibull-Lomax distribution are discussed.

A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

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