三参数Weibull分布的参数估计

PARAMETER ESTIMATION OF THE WEIBULL DISTRIBUTION WITH THREE PARAMETERS

In order to estimate the parameters of the Weibull distribution of the form Y = exp {-(x-c)/b]"} with Y representing the probability that a physical quantity X assumes a value exceeding x, two approaches are proposed for determining the parameters a,b and c from the observed sequences {xi} and {yi} The first approach is based on the requirement to minimize the sum and employs the oprimum seeking method and the linear regression method. The second approach requires bY}Y to be minimum. The function Y is expressed in the form of Taylor's expansion around the approximate values of the parameters and a succesive correction method is used to calculate the parameters. A practical application to estimating the extreme high and low temperatures corresponding to various return periods at Qingdao is given in the present paper.