%0 Journal Article %T The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework %A R. Caimmi %J Applied Mathematics %P 1-10 %@ 2152-7393 %D 2013 %I Scientific Research Publishing %R 10.4236/am.2013.411A4001 %X

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.

%K Standard Deviation %K n-Spaces %K Direction Cosines %K Quadrics %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=38298