On the relevance of convolution of uniform distributions to the theory of errors

Abstract

In recent years the uniform distributions and their convolutions find such applications that are relevant to geodesy-more precisely-to the modern theory of errors: (i) The convolutions of uniform distributions have been applied to the error distribution arising from data processing; (ii) Within the framework of geodesy, outliers were assumed to be distributed with uniform distribution. Bearing in mind these new developments and integrating these isolated topics, in this paper new closed formulae for the probability density and distribution functions of the sum of independent uniform random variables with unequal supports are derived. A brief outline of the relevance of convolutions of uniform distributions to the theory of errors related to astronomy and geodesy is given in historical setting. Along with these, the origin of uniform distribution is discussed with special emphasis on the root of the theory of errors.