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Abstract
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In this paper, A new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized halfnormal
(ZOLL-GHN) family with four parameters is introduced and studied. Useful representations and some mathematical
properties of the new family include moments, quantile function, moment Generating function are investigated. The
maximum likelihood equations for estimating the parameters based on real data are given. Different methods have been
used to estimate its parameters such as maximum likelihood, Least squares, weighted least squares, Crammer-von-Misers,
Anderson-Darling and right-tailed Anderson-Darling methods. We assesses the performance of the maximum likelihood
estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family
and fitness capability of this model, are illustrated by means of two real data sets.
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