Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution

Abstract

We consider a series of independent observations from a P-norm distribution with the position parameter μ and the scale parameter σ. We test the simple hypothesis H0:σ=σ1 versus H1: σ=σ2. Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of hσ which needs to satisfy the specific situation in SPRT method, and the approximate formula of the mean sample function is derived. Finally, a simulation example is given. The simulation shows that the ratio of sample size required by SPRT and the classic Neyman–Pearson N−P test is about 50.92% at most,38.30% at least.