Uncertain Hypothesis Test

In real life,it is usually necessary to decide whether some hypotheses about a problem are correct or not.To deal with these decision problems,there is a statistical tool in probability statistics called stochastic hypothesis test.Since the theoretical basis of stochastic hypothesis test is probability theory,it is used if the distribution function of the population is close enough to the real frequency.Most people believe that probability distribution is easy to obtain from the historical data,and then we should use probability theory.However,due to the complexity of problems and environments in practice,or the occurrence of emergencies(e.g.,flood,earthquake,war,accident,rumor,and even COVID-19),the distribution function obtained in most practical problems is,unfortunately,not close enough to the real frequency.In this case,it is unreasonable to use stochastic hypothesis test.In order to study how to judge whether some hypotheses are correct when the distribution function of the population is not close to the real frequency,this dissertation proposes uncertain hypothesis test in the framework of uncertainty theory for the first time,and focuses on how to test whether a set of observed data follow the normal uncertainty distribution.Furthermore,uncertain hypothesis test is applied to uncertain regression analysis,uncertain time series analysis and uncertain differential equation.In summary,this dissertation has the following innovations and contributions.· It first proposes uncertain hypothesis test,and presents a method to test whether a set of observed data follows the normal uncertainty distribution.· In uncertain regression analysis,it provides some methods to test whether the un-certain regression model is a good fit to the observed data and whether the linear regression model and regression coefficients are significant.· In uncertain time series analysis,it introduces a method to test whether the uncertain time series model is a good fit to the observed data.For the case that the fit is not good,an approach of difference is proposed.· In uncertain differential equation,it designs a method to test whether the uncertain differential equation is a good fit to the observed data.