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Abstract
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Based on the generalized log-logistic family (Gleaton and Lynch (2006))
of distributions, we propose a new family of continuous distributions with two extra
shape parameters called the exponentiated odd log-logistic family. It extends the class
of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (2006)) and
any continuous distribution by adding two shape parameters. Some special cases of
this family are discussed. We investigate the shapes of the density and hazard rate
functions. The proposed family has also tractable properties such as various explicit expressions
for the ordinary and incomplete moments, quantile and generating functions,
probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies,
extreme values and order statistics, which hold for any baseline model. The
model parameters are estimated by maximum likelihood and the usefulness of the new
family is illustrated by means of three real data sets
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