A flexible extension of skew generalized normal distribution
- PDF / 1,321,203 Bytes
- 21 Pages / 439.37 x 666.142 pts Page_size
- 66 Downloads / 222 Views
A flexible extension of skew generalized normal distribution Mahdi Rasekhi1 · G. G. Hamedani2 · Rahim Chinipardaz3
Received: 29 February 2016 / Accepted: 22 February 2017 © Sapienza Università di Roma 2017
Abstract We introduce an extension of the skew generalized normal distribution called shape-skew generalized normal distribution. The proposed distribution has certain type of flexibility which is different from those given in other flexible skew normal distributions. It possesses properties such as uni/bimodality, skewness, wider range of the Pearson’s excess kurtosis coefficient (γ2 ) with respect to skew generalized normal distribution and preserving the most desirable features of the skew generalized normal distribution. Some basic distributional properties of the new extension including moments, moment generating function, characterization and relation to other distributions are derived. Also, the multivariate case of our proposed distribution is introduced and some of its properties are studied. The suitability of our model is demonstrated via comparisons with other generalized models. Keywords Skew-symmetric distributions · Shape parameter · Skewing function · Moment · Stochastic representation · Skewness
B
Mahdi Rasekhi [email protected] G. G. Hamedani [email protected] Rahim Chinipardaz [email protected]
1
Department of Statistics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran
2
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, USA
3
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
123
M. Rasekhi et al.
1 Introduction Various types of skew-symmetric distributions have been proposed by many researchers in the literature. In general, there are four methods of constructing a skew-symmetric distribution with a symmetric density function [17]. One of these methods is perturbation of a symmetric density via skewing function, i.e. a skew probability density function (pdf) is created by multiplying a symmetric pdf with a skewing function. A skewing function is a function with range [0,1]. In fact, the starting point of all these studies was the skew-normal (SN) distribution introduced by [5], f (x; λ) = 2φ(x) (λx) , x ∈ R,
(1)
where φ and are the pdf and cumulative distribution function (cdf) of the standard normal, respectively. A random variable X with the above density is denoted by X ∼ S N (λ). [1] introduced a generalization of (1) with nice properties, called skew generalized normal distribution (SGN) with pdf of the form λ1 x f (x; λ1 , λ2 ) = 2φ(x) , x ∈ R. (2) 1 + λ2 x 2 Skew-curved normal distribution (SCN) is a SGN distribution with parameter λ2 = λ21 . A number of researchers proposed extension of this density such as [10,12,15,22]. Choudhury and Abdul Matin [10] added one parameter to SGN family and called it, extended skew generalized normal (ESGN) distribution with following density λ1 x f (x; λ1 , λ2 , λ3 )
Data Loading...
