Research On Skew Slash Distribution Based On Logistic Distribution

Since Azzalini proposed the definition of skew symmetric distribution in 1985,many scholars have studied skew normal distribution,skew Laplace distribution,skew t distribution,skew Logistic distribution and so on.In 1988,Kafadar firstly extended the normal distribution to the slash normal distribution that can handle heavy-tailed data.These shew slash distributions can better depict skew slash heavy-tailed data generated in real life compared to symmetric distributions such as normal distribution,Laplace distribution and Logistic distribution.The shew slash date is common in many dields.Therefore,it is necessary to study the shew slash distribution.Due to the lack of systematic research on slash and shew slash distributions based on Logistic distribution in existing papers.Therefore,in this paper we construct slash Logistic distribution.Then the paper proposes shew slash Logistic distribution based on the definitions of skew Logistic distribution and slash Logistic distribution.Finally,based on the definition of shew logistic distribution,the paper defines a class of shew symmetric Logistic distribution.And the shew slash heavy-tailed property of proposed distribution is proved by experiments.The main research contents of this paper are as follows:(1)In the first part,we construct random variables of slash Logistic,provide its definition,statistical properties and parameters estimation of slash Logistic distribution,and compare them with the density function curves of Logistic distribution and shew Logistic distribution.Finally,we demonstrate the heavy-tailed property of slash Logistic distribution by fitting actual data sets.(2)In the second part,based on the definitions of the slash Logistic and shew Logistic distributions,the paper constructs random variables of the slash skew Logistic distribution,and provides its definition,density function,basic properties,and parameters estimation.The density function curves of the slash skew Logistic distribution,shew Logistic distribution,and slash Logistic distribution are compared with each other.Finally,the skew slash heavy-tailed property of the distribution is proved by fitting actual data.(3)The third part defines a class of shew symmetric distributions based on shew Logistic distribution,including shew normal Logistic distribution,shew uniform Logistic distribution,and shew Laplace Logistic distribution,and they are applied to actual data to verify the skewness of the distribution.