离散变量参数UMA限中均匀数取值的研究

On Selecting the Value of Uniform Number in UMA Limits of the Parameter of Discrete Random Variables

本文用Jeffreys的无信息先验分布的Bayes方法与随机化的Fiducial方法,对UMA置信限中的均匀数u的取值问题进行了研究,结果表明,Mann建议u取1/2,对二项分布与有替换定时截尾的指数分布这是合适的,但对预定成功数或失败数的负二项分布,此值略为偏小,其相对误差与样本量n的关系为1/(2n+1)

Using Bayesian method of Jeffreys' noninformative prior and the randomized Fiducial method, the selection problem of value of uniform number in UMA limits of the parameter of discrete random variable is discussed. The results indicate, Mann' s proposition, uniform number u take 1/2, is suitable for the binomial distribution and the exponential distribution with time truncated test with replacement,but u = 1/2 is slightly small for the negative binomial distribution with predeterninate success number or fail number.The relative error is 1/(2n + 1) , where n is the sample size.