Abstract:

For the Weibull distribution parameter estimation， a pseudo-estimator of scale parameters is constructed， and the estimated parameter values can be obtained by finding the extreme point of relevant variables based on the principle that the right location parameter and shape parameter minimize the diversity of the scale parameter estimates associated with individual sample values. Essentially， parameter estimation extracts（overall）information based on specific patterns reflected by a set of data with uncertainty （random variable samples）. However， the pattern is statistical in nature rather than deterministic. In terms of the occurrence of extreme points in the related functions， the exact value of the estimater does not necessarily occur at the extreme point in a deterministic extreme point. It is shown that there is typically a deviation between the point where the exact parameter is located and the theoretical extreme point， and the accuracy and robustness of the parameter estimation method can be greatly improved by introducing an offset value in the minimum value criterion （modifying “the first derivative being equal to zero” to “the first derivative being equal to a value greater than zero”）. A large number of parameter estimation cases show that the range of the estimated value of the Weibull location parameter （true value is 1 000） is narrowed from 0~1 500 to 500~1 550 by taking an offset value of 0.1.

Key words: Weibull distribution, location parameter, parameter estimation, extreme value criterion, robustness