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 $\mu$ and the scale parameter $\sigma$ . We test the simple hypothesis $H_0:\sigma ={\sigma }_1$ versus $H_1:\sigma ={\sigma }_2$ . Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of $h\left(\sigma \right)$ 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 $\left(\text{N}-\text{P}\right)$ test is about $50.92\%$ at most, $38.30\%$ at least.