关于一种三参数Weibull分布的参数估计问题的研究

Research on a Parameter Estimate Problem of Three Parameter Weibull Distribution

在两参数Weibull分布参数估计方法的基础上,提出了一种求解三参数Weibull分布参数的极大似然估计数值方法.应用降阶思想将三元方程组转换成关于位置参数的一元方程,用二分法求解位置参数,继而通过两参数Weibull分布极大似然法估计形状参数和尺度参数.通过Monte-Carlo仿真,发现了各个参数估计值的变化关系,验证了该方法的有效性.

A new numerical algorithm was proposed to solve the extremely large likelihood estimation of the three parameter Weibull distribution on basis of the parameter estimation method of two parameter Weibull distribution.Firstly,according to the idea of order reducing,ternary likelihood equations can be turned into monadic equation of location parameters.And then,location parameters are solved with the dichotomy.Finally,maximum likelihood estimation of two-parameter Weibull distribution was used to estimate shape and scale parameter.The changing relations of each parameter estimations was discovered and the validity of this method was verified by the examples of Monte Carlo simulation.