2021/07/31 by Krzysztof Zajkowski, Zajkowski, Krzysztof
Decision Sciences · Mathematics · #FOS: Mathematics #Primary 60E05 #Probability (math.PR) #Probability and Risk Models #Secondary 46E30 #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2108.00272
openalex publication_date 2021/07/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal distribution. We will call its distribution the α-\it normal (Gaussian) distribution. We examine properties of this distribution in detail. We calculate moments and consider the moment problem of α-normal distribution. We derive the formula of its differential entropy and (exponential) Orlicz norm. % of α-normal random variables. Moreover, we define the joint distribution function of the multivariate α-normal distribution as a meta-Gaussian distribution with α-normal marginals. We consider also the limiting distribution as α tends to infinity.