Lwin T, Martin P J
Division of Mathematics and Statistics, CSIRO, Clayton, Victoria, Australia.
Biometrics. 1989 Sep;45(3):721-32.
The tolerances of individuals (insects, parasites) in a population have a frequency or probability distribution called a tolerance distribution. Many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions. A probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions. In this article, the existence and determination of the maximum likelihood estimates are investigated. An expectation-maximization (EM) algorithm for probits of mixtures is developed and it is shown that by application of the EM algorithm, the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions.
种群中个体（昆虫、寄生虫）的耐受性具有一种频率或概率分布，称为耐受性分布。生物测定研究中的许多耐受性分布可能是由相当异质的个体群体导致的，并且通常可以建模为多个标准单峰分布的混合。概率分析可以推广到耐受性分布是位置和尺度参数分布混合的情况。在本文中，研究了最大似然估计的存在性和确定方法。开发了一种用于混合概率的期望最大化（EM）算法，结果表明，通过应用EM算法，混合概率问题可以分解为一系列单个成分耐受性分布的概率问题。
