The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework
Author(s) R. Caimmi
ABSTRACT

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.

Cite this paper
R. Caimmi, "The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework," Applied Mathematics, Vol. 4 No. 11, 2013, pp. 1-10. doi: 10.4236/am.2013.411A4001.
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