Weibull distribution's parameters in electrical insulation reliability assessment

摘要

Many parametric models are used for equally distributed random variables (without taking into account the time dependence of the onset of the system event from covariates). The Weibull's distribution is considered to be practically justified for statistical analysis in technical systems. However, there is a problem of distribution parameters finding. The accuracy of distribution parameters's estimates depends on the accuracy of the estimates of the hypothetical distribution parameters and on the proximity of the hypothetical distribution to the true distribution. There are different methods and approaches to unknown parameters finding. There are probabilistic and statistical methods. All of them give an approximate solution to the problem. We consider various methods for finding out the parameters of the Weibull's distribution and suggest a method to replace the distribution function of a given distribution by its probabilistic estimate in this article. The article provides the examples of unknown parameters finding by means of the maximum likelihood methods, substitution of the distribution function, specialized mathematical program as well as and their comparative estimation.