Dangers and problems in calculating coefficients of a sum of exponential functions

The use of the computer in making calculations has led increasingly to the estimation of parameters of exponential functions from point experimental measurements. This involves the use of techniques such as logarithmic transformations and criteria (especially that of the least squares), of which the use is not always justified. Radioactivity measurements raise special problems as they are subject to a statistical distribution of the Poisson type. The authors propose a method based on the statistical criterion of "maximum likelihood" which permits tests of the number of exponentials from point measurements (in practice, this method is valid for one or two exponentials), and also the calculation of parameters more satisfactorily than customary methods.