Several Studies On Skew Distributions

Fitting data type affects the development of statistical distributions.Our adopted skew statistical distribution can fit some data more accurately especially after Azzalini proposed skew normal distribution. In recent years, some scholars have put forward alpha skew distribution and slash alpha skew distribution on the basis of skew distribution,but these distributions have small effect on data fitting effect with double or heavy tail.This paper tries to propose slash alpha skew Laplace distribution based on alpha skew Laplace distribution and estimates the parameters of this distribution through a large number of numerical simulation experiments and uses this distribution to fit practical data.Finally,judge the effect of evaluating the distribution by criteria on practical data fitting based on AIC/BIC model and verify the superiority of this statistical distribution.The research content of this paper includes following four aspects:1.Related definitions and properties of skewed distribution and alpha skew distribution have been studies. Some practical data fittings for skew distribution and alpha skew distribution have been made and use genetic algorithm to optimize log-likelihood function and estimate the parameters of partial distribution. Finally, use AIC and BIC rules to judge the good and bad of model.2. Random number generation algorithms have been offered for alpha skew distribution and alpha skew Laplace distribution. A large number of numerical experiments have been made and analyze the accuracy of parameter estimates by taking absolute error as reference point.3.Propose a new distribution for the shortages of alpha skew Laplace distribution:slash alpha skew Laplace distribution, discuss standard slash alpha skew Laplace distribution as well as the cumulative distribution function and related properties of slash alpha skew Laplace distribution respectively.Estimate the parameters of this distribution with moment estimation method and maximum likehood method under different sample volumes.4.Fit two groups of piratical data of students’ scores and fiber glass strength with slash skew alpha Laplace distribution and then analyze and the superiority of this distribution.