An alternative two-parameter gamma generated family of distributions: properties and applications

Abstract

Motivated by Torabi and Hedesh (2012), we propose a gamma extended family of distributions with two extra generator parameters. We present some special models and study general mathematical properties like asymptotes and shapes, ordinary and incomplete moments, generating and quantile functions, probability weighted moments, mean deviations, Bonferroni and Lorenz curves, asymptotic distributions of the extreme values, Shannon entropy, Rényi entropy, reliability and order statistics. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is determined. We define a new regression model based on the logarithm of the  roposed distribution. The usefulness of the new models is proved empirically in three applications to real data.

Keywords

• Estimation,Gamma distribution,Generated family,Maximum likelihood,Mean deviation,Moment,Quantile function

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