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The analysis and design of binary vapour‐liquid equilibrium experiments. Part I: Parameter estimation and consistency tests
Author(s) -
Sutton Thomas L.,
Macgregor John F.
Publication year - 1977
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450550519
Subject(s) - consistency (knowledge bases) , binary number , statistics , mathematics , estimation theory , function (biology) , maximum likelihood , confidence interval , likelihood function , statistical hypothesis testing , geometry , arithmetic , evolutionary biology , biology
When estimating the unknown parameters in semi‐empirical relationships from vapour‐liquid equilibrium experiments, it has been common practice to minimize the sum of squares of some arbitrary function of one or more of the measured variables (x, y, P, T) without regard to the statistical consequences of such a procedure. It is shown that because these arbitrary procedures do not fully account for the errors in all the variables in the functional relationship they can lead to poor parameter estimates when compared to a statistically sound procedure based on maximum likelihood. The analysis of some binary data sets and a simulation study based on one of them are used to demonstrate the kinds of errors that arise. Use of the maximum likelihood method of estimation also aids one in checking the adequacy of the model used, and in testing the consistency of the experimental data. This is accomplished by comparing the deviations between predicted and measured responses with their computed confidence limits.