The New Odd Log-Logistic Generalised Half-Normal Distribution: Mathematical Properties and Simulations

Abstract

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 {\it 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.