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The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework

DOI: 10.4236/am.2013.411A4001    7,210 Downloads   9,739 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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

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