Harris Extended Fréchet distribution: Properties, inference, and Applications to failure and waiting time data.

Abstract

We propose and develop the four-parameter Harris Extended Fréchet distribution. It is obtained by inserting the two-parameter Frechet distribution as the baseline in the Harris family and may be a useful alternative method to model income distribution and could be applied to other areas. We demonstrate that the new distribution can have decreasing, increasing and upside-down-bathtub hazard functions and that its probability density function is an infinite linear combination of Frechet densities. Some standard mathematical properties of the proposed distribution are derived, such as the quantile function, ordinary and incomplete moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, Renyi and ????-entropies, mean residual life and mean inactivity time, probability weighted moments, stress-strength reliability, and order statistics. We also obtain the maximum likelihood estimators of the model. The potentiality/flexibility of the new distribution is illustrated by means two applications to failure and waiting time data sets