A new distribution, the New Weibull-Pareto, is defined and studied. Various properties of the distributions are obtained and the method of maximum likelihood used to estimate the parameters of the distribution. The usefulness of the distribution has also been demonstrated by applying it to real life data.
The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.
In this paper, the authors present some complete monotonicity properties and some inequalities involving the (p, k)-analogue of the Gamma function. The established results provide the (p, k)-generalizations for some results known in the literature. Γ p,k (k) = 1.
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