定时截尾情形下BurrⅫ分布的参数估计及其检验

Parameter Estimation and Hypothesis Testing of BurrⅫDistribution under TypeⅠCensored Samples

在定时截尾情形下,讨论了BurrⅫ分布的形状参数、可靠度和失效率的极大似然估计,给出了极大似然估计的表达式,证明了极大似然估计的相合性和渐进正态性,并给出它的近似区间估计和假设检验公式,最后进行了参数估计的数值模拟。结果表明:形状参数的极大似然估计效果良好。

The maximum likelihood estimation of the shape parameter,reliability and failure rate on BurrⅫdistribution is discussed under typeⅠcensored samples,the expression of the maximum likelihood estimation is given,the consistency and asymptotic normality of the estimations are proved,its approximate interval estimation and hypothesis test formula are given,and finally,the numerical simulation of parameter estimations is carried out.The result shows that the maximum likelihood estimation of the shape parameter is effective.