Namespaces
Variants
Actions

Probable deviation

From Encyclopedia of Mathematics
Revision as of 17:27, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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=48303
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article