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Abstract
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We propose a new class of continuous distributions with two extra shape
parameters named the generalized odd log-logistic family of distributions.
The proposed family contains as special cases the proportional
reversed hazard rate and odd log-logistic classes. Its density function can be
expressed as a linear combination of exponentiated densities based on the
same baseline distribution. Some of its mathematical properties including
ordinary moments, quantile and generating functions, two entropy measures
and order statistics are obtained. We derive a power series for the
quantile function. We discuss the method of maximum likelihood to estimate
the model parameters. We study the behaviour of the estimators by
means of Monte Carlo simulations. We introduce the log-odd log-logistic
Weibull regression model with censored data based on the odd log-logisticWeibull
distribution. The importance of the new family is illustrated using
three real data sets. These applications indicate that this family can provide
better fits than other well-known classes of distributions. The beauty and
importance of the proposed family lies in its ability to model different types
of real data.
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