Extended Poisson-Frechet Distribution: Mathematical Properties and Applications to Survival and Repair Times

Abstract

In this paper, a new four parameter zero truncated Poisson Fréchet distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, residual and reversed residual life functions are investigated. The maximum likelihood method is used to estimate the model parameters. We assess the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling two real data sets to illustrate empirically its flexibility.

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

“…Tis parameter introduction has been shown to improve the ability of the developed distributions to ft varied real-life datasets with high degrees of skewness and kurtosis. Some of these newly developed distributions include the modifed alpha power transformed Weibull [1], general two-parameter [2], truncated inverse power Ailamujia [3], half-logistic modifed Kies exponential [4], truncated inverse power Lindley [5], Marshall-Olkin-Weibull-Burr XII [6], generalised unit half-logistic geometric [7], Chen Burr-Hatke exponential [8], modifed XLindley [9], arctan power [10], harmonic mixture Fréchet [11], sine-Weibull geometric [12], bounded odd inverse Pareto exponential [13], new extended Chen [14], power XLindley [15], extended Poisson-Fréchet [16], exponentiated Fréchet loss [17], Gompertz-Makeham [18], and logistic exponential [19] distributions.…”