Probable error
In statistics, probable error is a value describing the probability distribution of a given quantity. It defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside.[1] Thus it is equivalent to half the interquartile range, or the median absolute deviation.
Deprecated meaning
The term also has an older deprecated meaning, that is sometimes stated as the only meaning.[2][3] Probable error is denoted γ and defined as a fixed multiple of the standard deviation, σ, where the multiplying factor derives from the normal distribution, more specifically,[1][2]
This deprecated definition requires that at least the second moment of the distribution should exist, whereas the modern definition does not. One use of the term probable error in statistics is as the name for the scale parameter of the Cauchy distribution.
See also
References
- ↑ 1.0 1.1 Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
- ↑ 2.0 2.1 Zwillinger, D.; Kokosa, S. (2000) CRC Standard Probability and Statistics Tables and Formulae, Chapman & Hall/CRC. ISBN 1584880597 (Section 2.2.13)
- ↑ Yule, G.U.; Kendall, M.G. (1950) An Introduction to the Theory of Statistics, 14th Edition, Griffin. ISBN 0-85264-140-0 (Section 17.9)
