Baoding Liu

Uncertain hypothesis test is a statistical tool that uses uncertainty theory to determine whether some hypotheses are correct or not based on observed data. As an application of uncertain hypothesis test, this paper proposes a method to test whether an uncertain differential equation fits the observed data or not. In order to demonstrate the test method, some numerical examples are provided. Finally, both uncertain currency model and stochastic currency model are used to model US Dollar to Chinese Yuan (USD–CNY) exchange rates. As a result, it is shown that the uncertain currency model fits the exchange rates well, but the stochastic currency model does not.

This paper presents a statistical tool of uncertain significance test that uses uncertainty theory to test whether certain prespecified regression coefficients can be regarded as zero. A numerical example is given to illustrate how to test the significance of regression coefficients in an uncertain regression model. In order to compare uncertain significance test with stochastic significance test, both of these significance testing approaches are applied in studying the relationship between GDP and four indicators, including urban population scale, volume of foreign trade, fiscal expenditure, and water resource. The results show that uncertain significance test is more appropriate than stochastic significance test.

Uncertain queueing system is a waiting line in which the interarrival times and service times are both modeled by uncertain variables. This paper investigates four important performance characteristics of uncertain queueing system, including waiting time, idle time, total idle time and total busy time. The analytical formulas of uncertainty distributions of those performance characteristics are also derived separately.

Assume an uncertain process follows an uncertain differential equation, and some realizations of this process are observed. Parameter estimation for the uncertain differential equation that fits the observed data as much as possible is a core problem in practice. This paper first presents a problem of initial value estimation for uncertain differential equations and proposes an estimation method. In addition, the method of moments is recast for estimating the time-varying parameters in uncertain differential equations. Using those techniques, a COVID-19 spread model based on uncertain differential equation is derived, and the zero-day of COVID-19 spread in China is inferred.