The Alpha-Beta-Gamma Skew Normal Distribution and Its Application ()
ABSTRACT
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.
Share and Cite:
Wei, Z. , Peng, T. and Zhou, X. (2020) The Alpha-Beta-Gamma Skew Normal Distribution and Its Application.
Open Journal of Statistics,
10, 1057-1071. doi:
10.4236/ojs.2020.106060.