Hypothesis Testing For Scale Parameter In P-norm Distribution And Its Application

The P-norm distribution is an important kind of distribution,whose density function is given by (?) where ?(·)is gamma function,?=(?(3/p)/?(1/p))1/2,?(?>0)is scale parameter,? is the position parameter,and p(p>0)is the shape parameter.From the above formula,we can know that Laplace distribution(let p=1),normal distribution(let p=2),uniform distribution(let p??)and degenerate distribution(let p?0)are special cases of univariate P-norm distribution.In many cases,the error does not obey the normal distribution,and the P-norm distribution is closer to the reality.Therefore,it is of great significance to study P-norm distribution.However,almost all scholars have studied the parameter estimation of P-norm distribution and its related applications,but only few have studied the hypothesis testing of P-norm distribution.Since hypothesis testing is one of the important contents of statistical inference,this paper studies the problem of testing the scale parameter of P-norm distribution by three testing methods.The important contents are as follows:In chapter 2,the test of unknown scale parameters with P-norm distribution is studied by the method of likelihood ratio test.The asymptotic distribution and(approximate)density function of the likelihood ratio test statistic are obtained.Under the special cases,the density functions of Laplace distribution and normal distribution are given.Finally,some simulation examples are given to verify the effectiveness of this method.In chapter 3,the stopping rule and decision rule of sequential likelihood ratio test(SPRT)under the original hypothesis are given.The operational potential function of sequential probability ratio test is obtained,and the sample size of sequential probability ratio test is given.At the end of this chapter,a simulation example is given.It is shown that the average sample size required by the sequential probability ratio test of P-norm distribution is 38%?51%of that required by the classical Neyman-Pearson test.In chapter 4,the expression of the likelihood ratio test statistic under the original hypothesis is given,and the density function of the statistic is also obtained by means of the existence and asymptotic property of the likelihood estimation of the scale parameter.At the end of this chapter,a simulation example is given to further prove the rationality of the theoretical method.