Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

Abstract

In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution.

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.…”