The Mc-$\Gamma$ Distribution and Its Statistical Properties: An Application to Reliability Data

Abstract

The gamma distribution has been widely used in many research areas such as engineering, hydrology and survival analysis. We propose a new distribution, called the McDonald gamma distribution, which presents greater flexibility to model scenarios involving non-negative data. The new density function is re\-pre\-sen\-ted as a double linear combination of gamma densities. We also propose analytical expressions for some mathematical quantities: moments, moment ge\-ne\-ra\-ting function, log-moment, mean deviations, {Lorentz} and Bonferroni curves, order statistics, entropy and quantile function. The score function and the observed information matrix of this new distribution are derived. A real data set is used to illustrate the importance of the proposed model.