两个独立对数正态分布的中位数比的统计推断

Inferences for the Ratio of Medians of Two Independent Log-Normal Distributions

摘要: 本文主要研究了基于朴素似然法、两种广义枢轴量法、带Diffuse先验和独立Jeffreys先验的贝叶斯方法对两个独立对数正态分布中位数之比的统计推断。我们通过模拟比较了五种置信区间在覆盖率、平均长度和相对偏度方面的性能。结果表明，两种广义置信区间和基于Diffuse先验的贝叶斯方法在覆盖率上普遍较优。而基于似然方法和独立Jeffreys先验的置信区间的平均长度较短。此外，给出了参数的极大似然估计和贝叶斯后验估计。同时，给出了单边假设检验的广义p值和后验概率比。并以PM2.5的实际数据为例，说明了该方法的统计推断。

Abstract: In this paper, we concentrate on statistical inferences for the ratio of medians of two independent log-normal distributions based on naive likelihood approach, generalized variable approach with two generalized pivot quantities (GPQ) and Bayesian approach with Diffuse prior and Independence Jeffreys’ prior. We compare the performance of the five confidence intervals in terms of the coverage probabilities, average length and relative bias by using simulations. The results show that the Bayesian approach based on Diffuse prior and two kinds of generalized confidence intervals are generally preferred in terms of coverage probability. However, confidence intervals based on likelihood and Independence Jeffreys’ prior have shorter average length. We also give the maximum likelihood estimator and Bayesian posterior estimation of estimated parameter. Simultaneously, the generalized p-values and posterior probability ratio for a one-sided hypothesis test are proposed. The statistical inference is illustrated using a real data example about PM2.5.