Probable deviation
From Encyclopedia of Mathematics
mean deviation
A measure, 
, of dispersion for a probability distribution. For a continuously-distributed symmetric random variable 
the probable deviation is defined by
 | (*) |
where 
is the median of 
(which in this case is identical with the mathematical expectation, if it exists). For the normal distribution there exists a simple connection between the probable deviation and the standard deviation 
:
 |
where 
is the normal 
-distribution function. The approximate relation is 
.
Comments
The probably deviation is also called the mean error, [a2]. The phrase "mean deviation" is also used to denote the first absolute moment 
of the random variable around its median, [a1].
References
| [a1] | H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1966) pp. Sect. 15.6 |
| [a2] | Ph.H. Dubois, "An introduction to psychological statistics" , Harper & Row (1965) pp. 287 |
How to Cite This Entry:
Probable deviation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Probable_deviation&oldid=18784
Probable deviation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Probable_deviation&oldid=18784
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article