The normal distribution, an epistemological view

Keywords: knowledge, normal distribution, parameter estimation, Convolution Theorems, Central Limit Theorem, Bronstein von Mises Theorem


The role of the normal distribution in the realm of statistical inference and science is considered from epistemological viewpoint. Quantifiable knowledge is usually embodied in mathematical models. History and emergence of the normal distribution is presented in a close relationship to those models. Furthermore, the role of the normal distribution in estimation of model parameters, starting with Laplace’s Central Limit Theorem, through maximum likelihood theory leading to Bronstein von Mises and Convolution Theorems, is discussed. The paper concludes with the claim that our knowledge on the effects of variables in models or laws of nature has a mathematical structure which is identical to the normal distribution. The epistemological consequences of the latter claim are also considered.

Research Articles