Some Methodological Aspects Of Estimating The First Few Moments Of The Distribution Of The Gamma Ray Multipli

The non–identifiability of relevant parameters is often used as a decisive argument to reject the mathematical model and (or) experimental design. This study shows by means of an example that the argument is not compelling. The experiment to be considered has been designed to determine the first few moments of the distribution of the number of gamma rays, emitted after a nuclear fusion reaction of a particular type. This task of determining moments is so complicated that certain systematic errors cannot be completely avoided. In consequence, the moments are not identifiable with respect to the usual mathematical model and the current experiment (section 2). There is no sense in rejecting the model or the experiment on the basis of this non–identifiability. It is easy to construct a simple estimator for the first moment, with properties that are not too bad (section 2). The current estimation procedures seem to be more accurate. They can even be used to estimate some higher moments. The systematic errors cannot be avoided but are negligible in many reasonable situations (section 3 and 4). The actual analysis of the data is more complicated than suggested in the first four sections. Nevertheless these sections are relevant because the underlying model gives an adequate description of the observations after a preliminary reduction of the data. This fact is intuitively clear but can also be proved (section 5). A test–case suggests that even the standard errors provided by the current technology are reliable (section 6).