Recent Advances in Lifetime and Reliability Models

Recent Advances in Lifetime and Reliability Models

Introduction: Mathematicians and statisticians have made significant academic progress on the subject of distribution theory in the last two decades, and this area of study is becoming one of the ...
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Beta Generalized Models

Pp. 53-86 (34)

Gauss M. Cordeiro, Rodrigo B. Silva and Abraão D. C. Nascimento

Abstract

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.

Affiliation:

Universidade Federal de Pernambuco, Brazil.