对称指数分布的参数估计及其优良性

Parametric Estimate of Symmetric Exponential Distribution and Its Goodness

研究了双参数对称指数分布的参数估计问题,给出了2个参数的极大似然估计.在样本容量为奇数的情形,证明了样本中位数作为双参数对称指数分布位置参数的极大似然估计,具有无偏性与强相合性;尺度参数的极大似然估计具有强相合性.在样本容量为偶数的情形,证明了2个参数的任一极大似然估计均具有强相合性.

The estimate problem of the parameters for symmetrical exponential distribution with two parameters is investigated. The maximum likelihood estimators of the two parameters are obtained. In the situation that sample size is odd, the sample median, as the maximum likelihood estimator of location parameter, is proved to be unbiased and strongly consistent. The maximum likelihood estimator of scale parameter is proved to be strongly consistent. In the situation that sample size is even, the maximum likelihood estimators of location parameter and scale parameter are proved to be strongly consistent.