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Keywords
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Generated family, Maximum likelihood, Moment, Order statistic, Quantile
function, Survival analysis
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Abstract
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We introduce and study general mathematical properties of a new generator of
continuous distributions with three extra parameters called the odd log-logistic
logarithmic generated family of distributions. We present some special models and
investigate the asymptotes and shapes. The new density function can be expressed as a
linear combination of exponentiated densities based on the same baseline distribution.
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 discuss the estimation of the model parameters by
maximum likelihood. Further, we introduce the new family in long-term survival
models. We illustrate the potentiality of the proposed models by means of four
applications to real data.
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