The Alpha-Beta-Gamma Skew Normal Distribution and Its Application

• 作者: Tiankui Peng Xiaoya Zhou Zhengyuan Wei
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Skew Distribution Multimodal Distribution Alpha-Beta-Gamma Skew Normal Distribution Fisher Information Matrix
• 年，卷（期）: 2020,（6）
• 页码范围: 1057-1071
• 页数: 15页
• 分类号: O15

摘要

In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.