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Probits of Mixtures

T. Lwin and P. J. Martin
Biometrics
Vol. 45, No. 3 (Sep., 1989), pp. 721-732
DOI: 10.2307/2531679
Stable URL: http://www.jstor.org/stable/2531679
Page Count: 12
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Probits of Mixtures
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Abstract

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.

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