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

Francisco W. P. Marciano, A. D. C. Nascimento, M. Santos-Neto, G. M. Cordeiro


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.

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International Journal of Statistics and Probability   ISSN 1927-7032(Print)   ISSN 1927-7040(Online)

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