Journal of Data Science

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.

In this paper Zografos Balakrishnan Power Lindley (ZB-PL) distribution has been obtained through the generalization of Power Lindley distribution using Zografos and Balakrishnan (2009) technique. For this technique, density of upper record values exists as their special case. Probability density (pdf), cumulative distribution (cdf) and hazard rate function (hrf) of the proposed distribution are obtained. The probability density and cumulative distribution function are expanded as linear combination of the density and distribution function of Exponentiated Power Lindley (EPL) distribution. This expansion is further used to study different properties of the new distribution. Some mathematical and statistical properties such as asymptotes, quantile function, moments, mgf, mean deviation, renyi entropy and reliability are also discussed. Probability density (pdf), cumulative distribution (cdf) and hazard rate (hrf) functions are graphically presented for different values of the parameters. In the end Maximum Likelihood Method is used to estimate the unknown parameters and application to a real data set is provided a. It has been observed that the proposed distribution provides superior fit than many useful distributions for given data set.