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.

R. Caimmi, "The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework,"

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