Reflexions on the kurtosis of samples of errors

This study, applicable to large samples of observational errors, examines the causes that may lead to curves of probability density functions exhibiting the phenomenon of kurtosis. The instability, which may be of a continuous or discontinuous nature, of an observed reference or target results in mixtures of individual distributions having different means. Hence, it may happen that the total mixture has a platykurtic tendency. However, other experimental changes can result in mixtures of distributions of differeing variances thereby leading to leptokurtosis of the combined sample. It is demonstrated how the presence of both kurtoses can produce quasi-normal curves. The dichotomy of 2252 output errors of groups of watt hour meters, subjected to varying environmental effects, illustrates the application of the theory and formulae to establish that the total set is a mixture of discrete normal and modulated distributions having different means and variances.