双边定时截尾样本下广义逆指数分布形状参数的估计

先给出了广义逆指数分布在双边定时截尾样本下形状参数的最大似然估计,并不能得到估计的显式表达式,但证明了参数在(0,+∞)上最大似然估计是唯一存在的.其次提出用EM算法求出形状参数的估计且该估计具有良好的收敛性,还给出了形状参数的EM估计的渐近方差和近似置信区间;最后通过数值模拟,对形状参数的最大似然估计和EM估计的效果进行了比较,说明了用EM算法求形状参数的估计是可行的,并且模拟效果相对比较好.

Estimation of the Shape Parameter for Generalized Inverted Exponential Distribution Under Bilateral Type-Icensored Sample

Firstly,we can not obtain the explicit expression of the parameter through the maximum likelihood estimation of the shape parameter studied in the generalized inverted exponential distribution under bilateral type-ICensored Sample,but it can be proved that the maximum likelihood estimation in(0,∞) is unique.Secondly,we may calculate the estimated value of the shape parameter,which has good convergence,by the way of EM algorithm,and the asymptotic variance and approximate confidence interval of the shape parameter are also given.Finally,by comparing the maximum likelihood estimation and EM estimation of the parameter according to numerical simulation,we learn that the EM algorithm is an effective method for parameter estimation,and the simulation effect is relatively good.