序约束下双参数指数分布的Fiducial参数估计

Fiducial Parameter Estimation on the Two-Parameter Exponential Distribution under the Order Restrictions

利用Fiducial统计推断的方法,给出双参数指数分布参数的Fiducial模型,然后基于参数的Fiducial模型给出两总体序约束下参数的Fiducial分布,得到序约束条件下未知参数的Fiducial参数估计的具体解析式,同时给出两总体序约束下未知参数的参数估计的数值解.对于总体个数大于2的情况,根据Fiducial模型给出相应的参数估计的数值计算方法,并进行数值模拟,结果证明由这种数值方法所得到的数值解的误差是可以接受的.

The Fiducial model in the two-parameter exponential distribution is given on the basis of the Fiducial estimation method. The Fiducial distribution under the two global order restrictions is presented. The exact expressions to estimate the Fiducial parameters under the order restrictions can be obtained. Since the solutions to the expressions are complex, the parameter estimation solutions under the two global order restrictions are presented. If the global number is over two, the exact expressions cannot be given. The parameter estimation computing method based on the Fiducial model and numerical simulations is proposed. It is shown that the error that is caused by this method can be accepted.