The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications

Year 2016, Volume: 45 Issue: 6, 1781 - 1803, 01.12.2016

Gauss M. Cordeiro Morad Alizadeh Edwin M.m. Ortega Luis H. Valdivieso Serrano

Abstract

We study some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the
Zografos-Balakrishnan odd log-logistic family. We present some special
models and investigate the asymptotes and shapes. The density function of the new family 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, Shannon and
Rényi entropies and order statistics, which hold for any baseline model,
are determined. We estimate the model parameters by maximum likelihood. Two real data sets are used to illustrate the potentiality of the
proposed family

Keywords

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

References

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