The Three-Parameter Lognormal Distribution and Bayesian Analysis of a Point-Source Epidemic
The Three-Parameter Lognormal Distribution and Bayesian Analysis of a Point-Source Epidemic
复制标题
一次点源疫情的三参数对数正态分布与贝叶斯分析
DOI：
10.1080/01621459.1963.10500833
复制
发表时间：
1963
影响因子：
3.7
通讯作者：
B. Hill
中科院分区：
文献类型：
--
作者：
B. Hill
摘要探讨了三参数对数正态分布ln(t - γ) ~ N（μ, σ2）的似然函数的一些异常特征。特别地，我们证明了当（γ, μ, σ2）逼近（t(1), -∞,+∞）时，任意样本t（1，…，tn）的似然函数趋于∞的路径存在，其中t(1)是ti的最小值，因此在有意义的意义上，这是最大似然估计。然后从贝叶斯的角度考虑估计，并探讨了一些自然后验分布。提出了一种点源流行病的统计模型，并将所建立的理论用于估计发病时间和其他参数。
Abstract Some unusual features of the likelihood function of the three-parameter lognormal distribution ln(t – γ)∼N(μ, σ2) are explored. In particular, it is shown that there exist paths along which the likelihood function of any sample t 1, …, tn tends to ∞ as (γ, μ, σ2) approaches (t (1), – ∞, + ∞), where t (1) is the smallest of the ti , and hence that in a meaningful sense this is the maximum-likelihood estimate. Estimation is then considered from a Bayesian point of view, and some natural posterior distributions are explored. A statistical model for a point-source epidemic is presented, and the theory developed is used in estimating the time of onset and other parameters.