Recent Advances in Lifetime and Reliability Models

Beta Generalized Models

Author(s): Gauss M. Cordeiro, Rodrigo B. Silva and Abraão D. C. Nascimento

Pp: 53-86 (34)

DOI: 10.2174/9781681083452120010005

* (Excluding Mailing and Handling)


The beta transformation gives a great variety of shapes which allow to model symmetric, skewed and bimodal shaped densities. Such procedure generates what we call the beta generalized (beta-G) family of distributions. This chapter presents a survey on the beta-G models and their mathematical properties. We present some explicit expressions for the ordinary and incomplete moments, probability weighted moments, cumulants and generating function, mean deviations, entropies and order statistics.

Keywords: Beta-G model; Entropy; Mean deviation; Moment; Probability weighted moment; Regression model.

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