A New Extension of the Normal Distribution

Journal of Data Science

article

Maria do Carmo S. Lima¹  Gauss M. Cordeiro¹  Edwin M.M. Ortega² 

[1] Departamento de Estatística, Universidade Federal de Pernambuco - UFPE;Departamento de Ciências Exatas, Universidade de São Paulo - USP

关键词: Gamma distribution;    Maximum likelihood estimation;    Mean deviation;    Normal distribution;    Quantile;   

DOI  :  10.6339/JDS.201504_13(2).0009

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

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.

【 授权许可】

CC BY