升降法参数估计公式的理论分析与计算机模拟

Theoretical Analysis and Computer Simulation on Parameter Estimation Formula of Up-and-Down Method

对升降法的参数估计公式进行了理论分析推导,得到与原估计公式不同的一组参数值,并对其进行了分析修正;应用Monte Carlo方法进行了升降法的大样本模拟试验,对比了不同样本量、同一模拟试验数据、使用不同参数值计算的标准差及其相对误差。结果表明:升降法参数估计公式中的两个参数来源不清,是经验性数据,经分析修正后的参数值来源清晰,模拟结果也表明其对标准差的估计精度较高。

In this paper, another parameter estimation formula by theoretical analysis and formula derivation on up-and-down method were obtained, and the parameter estimation formula was also corrected. A large number of simulation experiments on up-and-down method have been done using the Monte Carlo method, as well as the standard deviations and fractional errors of different parameter values with the same simulation test data and different samples were compared. It shows that the source of two parameters in the old parameter estimation formula is unclear, they are empirical parameters, but the source of two parameters in the corrected parameter estimation formula is clear, the result of simulation test using the corrected parameter estimation formula shows that the estimation accuracy of standard deviation is better.