Wrapped distributions and measurement errors |
| |
Authors: | Prof Dr W Stadje |
| |
Institution: | (1) Fachbereich Mathematik, Universität Osnabrück, Albrechtstr. 28, D-4500 Osnabrück |
| |
Abstract: | Summary For a random variableX and >0 letU
![agr](/content/w81nx79736182635/xxlarge945.gif) n
(X)–X, wheren
(x)=n Z iffx (n – /2,n + /2]. Random variables of this type are important in the theory of measurement errors. We derive formulas for the distribution ofU
and apply them to the case X N( , 2). General conditions for the unimodality ofU
are given. The correlation of the measurement errorsX–E (X) andU
(X) is seen to beO ( j) withj depending on the smoothness and asymptotic behavior of the density ofX. This gives a precise sense to the assertion that scale errors upwards and downwards are averagely well-balanced. In the normal case the density ofU
is shown to be constant up to
, as ![agr](/content/w81nx79736182635/xxlarge945.gif) 0. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|