定时截尾数据Pareto分布参数的Bayes估计

Bayesian estimation of Pareto distribution parameter under entropy loss based on fixed time censoring data

研究定时截尾数据情形下Pareto分布参数θ的Bayes估计和可容许性.给出熵损失函数的定义,取损失函数为熵损失函数,通过计算求出定时截尾情形下的熵损失函数,从而给出了Pareto分布参数θ的Bayes估计的一般形式;在给出先验分布为Gamma分布的条件下,计算出参数θ的后验密度,进而得出了参数θ的Bayes估计的精确形式,证明了所得到的参数θ的Bayes估计的可容许性.

In order to investigate the Bayesian estimation of Pareto distribution parameter on fixed time censoring data, this paper introduces the definition of entropy loss function by taking the loss function as entropy loss function. Through the calculations of above functions, the general form of Bayesian estimation of Pareto distribution parameter is obtained. Under the conditions of prior distribution as Gamma distribution, calculating the posterior density, the exact form of estimation is then given. In addition, the paper proves that the Bayesian estimation is admissible.