Several Skew-Slash Statistical Distributions

Since the fundamental properties of the skew normal distribution were introduced by Azzalini, many investigations have been made about the skew distributions based on certain symmetric probability density functions. These classes of the skew symmetric distributions include the original symmetric distribution and have some properties like original one and yet are skew.This paper is consisted of four parts:In the first part, we first introduce a skew slash normal distribution and a skew Cauchy distribution, in which a slash normal distribution is often viewed as a challenging distribution for a statistical procedure. By setting parameters, a skewed version of the slash distribution can be defined and its several properties are derived. As a typical application, we give also an example to which a multivariate skew slash distribution can be used in simulation studies.In the second part, we discuss slash t distributions and skew slash t distributions. It is well known that the limiting distribution of the t distribution, as the degrees of freedom tend to infinity, is the normal distribution. According to this fact, the slash t distribution and the skew slash t distribution can then be derived from the slash normal distribution and the skew slash normal distribution, respectively. We study statistical properties of these distributions such as invariance under linear transformations and marginal distributions.In the third part, we define a new distribution:slash Laplace distribution, based on the symmetric and heavy-tailed properties of the Laplace distribution. Its probability density function and cumulative distribution function are derived and its parametric estimation methods are discussed. In addition, it is compared with the Laplace distribution and asymmetric Laplace distribution.Finally, we apply some of these distributions to the real data sets and give corresponding analysis and conclusions.