The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework

The current attempt is aimed to outline the geometrical framework of a well known statistical problem, concerning the explicit expression of the arithmetic mean standard deviation distribution. To this respect, after a short exposition, three steps are performed as 1) formulation of the arithmetic mean standard deviation as a function of the errors which, by themselves, are statistically independent; 2) formulation of the arithmetic mean standard deviation distribution as a function of the errors; 3) formulation of the arithmetic mean standard deviation distribution as a function of the arithmetic mean standard deviation and the arithmetic mean rms error. The integration domain can be expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the symmetry axis coincides with a coordinate axis. Finally, the solution is presented and a number of (well known) related parameters are inferred for sake of completeness.