Exponentiated $T$-$X$ Family of Distributions with Some Applications

Abstract

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 Weibull- exponential 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 expo- nentiated Weibull-exponential distribution is assessed by applying it to three real data sets and comparing it with other distributions. The exponentiatedWeibull-exponential distribution is found to adequately fit left-skewed and right-skewed data sets.