Estimation of uncertainty distribution function by the principle of least squares

Abstract

In order to estimate the unknown parameters in an uncertainty distribution function, this article uses the principle of least squares that minimizes the sum of the squared deviations between the uncertainty distribution and the empirical distribution of the observed data. After that, the principle of least squares is applied to determining the uncertain disturbance term of uncertain regression model and uncertain time series model, and estimating the unknown parameters in uncertain differential equation. Finally, in order to illustrate the proposed method, some real-world examples are provided, including PetroChina stock price, electricity price, grain yield, China’s population, and beef price.