The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework  

作　　者：R. Caimmi 

机构地区：[1]Physics and Astronomy Department, Padua University, Padova, Italy

出　　处：《Applied Mathematics》2013年第11期1-10,共10页应用数学（英文）

摘　　要：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.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.

关 键 词：Standard Deviation n-Spaces Direction Cosines QUADRICS 

分 类 号：O1[理学—数学]