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Weibull distribution is one of the most widely applied statistical distributions in various fields, especially in reliability and lifetime analysis. It has monotonically increasing, monotonically decreasing, and constant hazard rate; these however, partly limits its applications. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, a new family of continuous distributions based on the Weibull random variable called the Reflected Kumaraswamy Weibull-X {Exponential} family of distributions was introduced. General statistical properties of the new family were established and discussed, general expressions for the ordinary and incomplete moments, the generating function, quantile function, and order statistics were also provided. The maximum likelihood method of estimation was used to estimate the model parameters. In addition, the asymptotic confidence intervals for the parameters were derived from the Fisher information matrix. Real-life application to three datasets were provided and comparison was made with respect to some existing families of distributions in the literature. [ABSTRACT FROM AUTHOR]

The Lomax distribution was extended in this paper using the Topp–Leone family of distributions. Some of its specific structural properties were established and the model parameters were estimated using maximum likelihood estimation method. The usefulness of the Topp–Leone Lomax distribution was demonstrated using an airbone communication transceiver dataset and comparison were made with respect to the Topp–Leone Burr XII, Topp–Leone Flexible Weibull and Lomax distributions. [ABSTRACT FROM AUTHOR]

In this paper, a new compound continuous distribution named the Gompertz Fréchet distribution which extends the Frèchet distribution was developed. Its various statistical properties were also derived and estimation of model parameters was considered using the maximum likelihood estimation method. The application of the Gompertz Fréchet distribution was provided using real-life data sets and its performance was compared with Gompertz Weibull distribution, Gompertz Lomax distribution and Gompertz Burr XII distribution. [ABSTRACT FROM AUTHOR]

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution. [ABSTRACT FROM AUTHOR]