Sequential Test Of Fuzzy Hypotheses

Fuzzy hypothesis testing problem refers to introduction of fuzziness into the classical hypothesis testing theory,that is,the fuzzy concept is introduced in the sample observation values or hypothesis to be tested.As an extension of the classical statistical hypothesis testing method,fuzzy hypothesis testing is considered as an important method for dealing with the fuzzy concept in statistical inference and statistical decision making.Sequential test as a branch of mathematical statistics,"sequential sampling plan" and statistical inference problem are studied by using samples obtained from the sampling plan,which has characteristics of simple algorithm and high retrieval efficiency.Time is a key factor to be considered in time sequential planning,the shortcoming of general sequential method is compensated,which can effectively avoid phenomenon such as waste of resources caused by too long sampling time.In this paper,the crisp sample data is used to combine fuzzy hypothesis problem with the sequential test method.The sequential test theory of fuzzy hypothesis is developed,sequential analysis method is enriched under fuzzy environment too.Firstly,fuzzy hypothesis problem of exponential distribution parameter is studied by the sequential probability ratio test method,and approximate calculation formula of average sample size required for the test is given.Secondly,under the view point of Bayesian statistical decision,Bayesian sequential testing problem of fuzzy hypothesis with loss function and without loss are discussed respectively,Poisson distribution parameters is inferred by testing and specific Bayesian stopping decision rule is given.Finally,based on the general life distribution,Bayesian time sequential decision method is studied and fuzzy hypothesis Bayesian time sequential test problem of Weibull distribution scale parameter is considered,in which the loss function includes two parts:test cost and misjudgment loss.In addition,numerical simulations are carried out for the above test theories,numerical example results show that the method is feasible and effective.Also compared with the classical fixed sample size test,both general sequential test method and Bayesian sequential test method can effectively save samples,at the same time,goals of reducing test cost and improving test efficiency are achieved.