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Abstract
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The new distributions are very useful in describing real data sets, because these distributions are
more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the
best-suited statistical distribution for modeling data is very important. In this paper, A new class of
distributions called the New odd log-logistic generalized half-normal (NOLL-GHN) family with four
parameters is introduced and studied. This model contains sub-models such as half-normal (HN),
generalized half-normal (GHN )and odd log-logistic generalized half-normal (OLL-GHN) distributions.
some statistical properties such as moments and moment generating function have been calculated. The
Biases and MSE’s of estimator methods such as maximum likelihood estimators , least squares estimators,
weighted least squares estimators, Cramer-von-Mises estimators, Anderson-Darling estimators and right
tailed Anderson-Darling estimators are calculated. The fitness capability of this model has been
investigated by fitting this model and others based on real data sets. The maximum likelihood estimators
are assessed with simulated real data from proposed model. We present the simulation in order to test
validity of maximum likelihood estimators.
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