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Title
The beta Marshall-Olkin family of distributions
Type Article
Keywords
Generated family; Marshall-Olkin family; Maximum likelihood; Moment; Order statistic; Quantile function; Rényi entropy
Abstract
We study general mathematical properties of a new generator of continuous distributions with three extra shape parameters called the beta Marshall-Olkin family. We present some special models and investigate the asymptotes and shapes. The new density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We discuss the estimation of the model parameters by maximum likelihood and illustrate the flexibility of the family by means of two applications to real data
Researchers Morad Alizadeh (First researcher) , Gauss Cordeiro (Second researcher) , Edleide Brito (Third researcher) , Clarice B. Demétrio (Fourth researcher)