Exponential depression as a test of estimated decay parameters

Abstract

A new test for judging the goodness of estimated decay parameters is presented. The test is based on the fact that a convolution is invariant under exponential depression. In the absence of significant error the estimated parameters will then remain constant as the degree of depression is varied over a finite range. In the presence of error, the parameters will vary. Up to now, no test has existed to see if moment index displacement corrects errors to a satisfactory extent in any given analysis. It has always been necessary to have some a priori knowledge of the type of error that limited the analysis. The test presented here removes that requirement. In addition, it is shown that the test performs better than a visual inspection of residual and autocorrelation plots in judging analyses when decays are closely spaced, even in the absence of nonrandom errors. The test is useful in accepting or rejecting analyses, with or without automatic error correction, in helping to discriminate between different models of sample decay, and in tuning pulse fluorometers for optimal performance. The test is, in principle, independent of the method of moments; it may be used with any method which needs only a small amount of computer time, and which is a statistically resistant procedure. © 1982 American Institute of Physics.