Journal of Data Science

istribution of Lindley distribution constructed by combining the cumulative distribution function (cdf) of Lomax and Lindley distributions. Some mathematical properties of the new distribution are discussed including moments, quantile and moment generating function. Estimation of the model parameters is carried out using maximum likelihood method. Finally, real data examples are presented to illustrate the usefulness and applicability of this new distribution.

Providing a new distribution is always precious for statisticians. A new three parameter distribution called the gamma normal distribution is defined and studied. Various structural properties of the new distribution are derived, including some explicit expressions for the moments, quantile and generating functions, mean deviations, probability weighted moments and two types of entropy. We also investigate the order statistics and their moments. Maximum likelihood techniques are used to fit the new model and to show its potentiality by means of two examples of real data. Based on three criteria, the proposed distribution provides a better fit then the skew-normal distribution.