|
Abstract
|
We introduce and study general mathematical properties of a new generator of continuous
distributions with three extra parameters called the new generalized odd log-logistic family of
distributions. The proposed family contains several important classes discussed in the literature
as sub-models such as the proportional reversed hazard rate and odd log-logistic classes. Its
density function can be expressed as a mixture of exponentiated densities based on the same
baseline distribution. Some of its mathematical properties including ordinary moments, quantile
and generating functions, entropy measures and order statistics, which hold for any baseline
model, are presented. We also present certain characterization of the proposed distribution and
derive a power series for the quantile function. We discuss the method of maximum likelihood
to estimate the model parameters. We study the behavior of the maximum likelihood estimator
via simulation. The importance of the new family is illustrated by means of two real data sets.
These applications indicate that the new family can provide better fits than other well-known
classes of distributions. The beauty and importance of the new family lies in its ability to model
real data.
|