Testing Goodness-of-fit For A Skew-t Distributions Based On Empirical Likelihood Ratio

In data processing,the distribution of many actual data is often skewed.The skew-t distribution family is a kind of statistical model that can fit the skew-distribution data.Skew-t distribution can not only describe the Skew,unimodal and other characteristics of the data,but also describe the longer tail distribution than the normal distribution.Skew-t distribution has been widely used in economics,medicine,biology and social research.Therefore,the research on the goodness of fit of Skew-t distribution has important theoretical and practical significance.Likelihood ratio test is a commonly used hypothesis test method,many commonly used test methods with good properties can be derived from the likelihood ratio method.The famous nyman-person lemma points out that the likelihood ratio test is the consistent optimal test for the simple null hypothesis and the simple alternative hypothesis.However,for the hypothesis test of non-parametric distribution group,as the specific form of the population distribution is unknown,the likelihood ratio test method of the parameter distribution group is not suitable,so it is necessary to find a new test method.Empirical likelihood method is an effective non-parametric statistical method and has been widely concerned by statisticians.This paper mainly studies the goodness of fit test of Skew-t distribution based on empirical likelihood method.The first chapter mainly introduces the research status of Skew-t distribution and empirical likelihood method at home and abroad.The second chapter mainly introduces the concept and related properties of Skew-t distribution,and introduces the basic principle and method of empirical likelihood.In chapter 3,the goodness of fit test of Skew-t distribution is constructed based on empirical likelihood method.We first use maximum likelihood estimation to estimate unknown parameters in the distribution,then build test statistics according to the methods introduced by Vexler and Gurevich,give a method to determine the negative field,and prove some asymptotic properties of test statistics.In chapter 4,the critical value of the test and the estimation of the probability of making the first type of error are obtained by Monte Carlo simulation,and compared with the EDFT test based on the empirical distribution function.The results show that the test proposed in this paper can control the probability of making the first kind of error well and has a good test effect.Therefore,this method has feasibility and practical application value.Two examples are analyzed to verify the practicability of our method.