Errors in Inspection: Integer Parameter Maximum Likelihood in a Finite Population
研究了在有限批次产品检验中，有放回和无放回抽样对最大似然估计的影响，提出了一种同时优化整数和标量参数的方法，并发现估计结果在多数情况下稳定。
Abstract In a probability model for possible errors in the inspection of a finite lot containing defective items, it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement. These changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter. A new method for the bounding of the integer solution is introduced. The results show that the parameter estimates in the inspection model are generally stable under wide changes in the sampling framework. Conditions for instability of the solution are identified. Some apparently new relations for discrete distributions are derived in the process of the investigation.