TITLE:
The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework
AUTHORS:
R. Caimmi
KEYWORDS:
Standard Deviation; n-Spaces; Direction Cosines; Quadrics
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11D,
October
22,
2013
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.