The Kummer Beta Normal: A New Useful-Skew Model

Journal of Data Science

article

Rodrigo R. Pescim¹  Saralees Nadarajah¹ 

[1] ESALQ – Universidade de Sao Paulo and 2University of Manchester

关键词: Bayesian analysis;    Kummer beta generalized distribution;    Maximum likelihood method;    Moment;    Normal distribution;    Order statistic;   

DOI  :  10.6339/JDS.201507_13(3).0006

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

The normal distribution is the most popular model in applications to real data. We propose a new extension of this distribution, called the Kummer beta normal distribution, which presents greater flexibility to model scenarios involving skewed data. The new probability density function can be represented as a linear combination of exponentiated normal pdfs. We also propose analytical expressions for some mathematical quantities: Ordinary and incomplete moments, mean deviations and order statistics. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis. Likelihood ratio statistics and formal goodnessof-fit tests are used to compare the proposed distribution with some of its sub-models and non-nested models. A real data set is used to illustrate the importance of the proposed model.

【 授权许可】

CC BY