关键词: P-Ⅲ参数计算, 函数置换, 最小二乘原理, 方向搜索法, 误差控制

Abstract: The integration of P-Ⅲ density function is very difficult, and its estimated parameters are generally with large uncertainty. By substituting the exponential function in the density function (in a small interval) with the cubic function, we realized the integration of density function, and got the cumulative probability in theory and built an objective function on the sum of squared errors. Since the objective function is constituted by several compound functions with variable coefficients, we can't get the relation equation with simple derivation, so a solution by the direction search method is put forward. Due to the special law of the function substitution error, we can make effective control on accuracy according to the accuracy criteria. The P-Ⅲ parameter got by this way can achieve the best fitting between the frequency curve and the sample points. Depending on simple excel template, we can also calculate the theoretical value of the P-Ⅲ distribution with various parameters.

Key words: P-Ⅲ parameter calculation, function substitution, least squares, direction search method, error control