Double Sequential Weighted Probability Ratio Test Based On Rayleigh Distribution

Rayleigh distribution is the probability distribution of positive continuous random variables. When a random vector is analyzed into its orthogonal 2-dimensional vector components. Assuming that each component is uncorrelated, normally distributed with equal variance, and zero mean, then the vector magnitude will be characterized by a Rayleigh distribution.This article mainly studies the one-sided composite hypotheses test under the Rayleigh distribution. In Chapter 2, we develop the method of double sequential weighted probability ratio test for one-sided composite hypotheses, and evaluate the performance of SPRT,2-SPRT, Chen method in one-sided composite hypotheses test.The result shows that average sample size of the method of double sequential weighted probability ratio test are smaller than the SPRT method,2-SPRT method, Chen method. In Chapter 3,we develop the method of double sequential weighted probability ratio test for three hypoth-esis test problem under the Rayleigh distribution. The result shows that average sample size of the method of double sequential weighted probability ratio test are smaller than the Soble-Wald, Whitehead-Brunier method. This suggests that the one-sided compos-ite hypotheses test problem under the Rayleigh distribution, using the double sequential weighted probability ratio method is more advantage.