Jixie qiangdu (Jan 2023)
INTERVAL ESTIMATION OF WEIBULL DISTRIBUTION BASED ON MODIFIED PIVOTAL VARIABLE METHOD (MT)
Abstract
To solve the problems of complex calculation and weak applicability of the traditional interval estimation methods such as Weibull distribution with the different parameters, a simple interval estimation method suitable to the conditions of multi-parameters was proposed. Through the expression of Weibull distribution, the pivotal-variable obeying chi-square distribution was obtained and the degrees of freedom were modified. Combined with the point estimation results from maximum likelihood estimation and the empirical estimation shape parameter in the Weibull distribution, the interval estimation method of two parameters in Weibull distribution was established. The confidence of proposed interval estimation method was verified by Monte Carlo simulation, and the applicability of the method on different parameters was also analyzed. Furthermore, comparisons with the results computed from traditional least square and maximum likelihood estimation methods were carried out by using simulation. Simulation results indicated that the modified pivotal-variable method has simple calculation process and small deviation from predefined nominal confidence with the different parameters. Therefore, it can be concluded that proposed method executes the more effective estimation than the traditional methods.
