Difference between revisions of "Gini average difference"
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| − | + | A magnitude characterizing the [[Dispersion|dispersion]] of the values of a random variable $ X $. | |
| + | It was introduced by C. Gini in 1912 and is defined by the formula | ||
| − | + | $$ | |
| + | \Delta = \int\limits _ {- \infty } ^ \infty \int\limits _ {- \infty } ^ \infty | ||
| + | | x - y | dF ( x) dF ( y) , | ||
| + | $$ | ||
| − | where | + | where $ F ( \cdot ) $ |
| + | is the distribution function of the random variable. Another variable which is also occasionally considered is the Gini dispersion coefficient | ||
| + | |||
| + | $$ | ||
| + | G = | ||
| + | \frac \Delta {2 \mu } | ||
| + | , | ||
| + | $$ | ||
| + | |||
| + | where $ \mu $ | ||
| + | is the [[Mathematical expectation|mathematical expectation]] of the random variable $ X $. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> M.G. Kendall, A. Stuart, "The advanced theory of statistics. Distribution theory" , '''3. Design and analysis''' , Griffin (1969)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> M.G. Kendall, A. Stuart, "The advanced theory of statistics. Distribution theory" , '''3. Design and analysis''' , Griffin (1969)</TD></TR></table> | ||
Latest revision as of 19:42, 5 June 2020
A magnitude characterizing the dispersion of the values of a random variable $ X $.
It was introduced by C. Gini in 1912 and is defined by the formula
$$ \Delta = \int\limits _ {- \infty } ^ \infty \int\limits _ {- \infty } ^ \infty | x - y | dF ( x) dF ( y) , $$
where $ F ( \cdot ) $ is the distribution function of the random variable. Another variable which is also occasionally considered is the Gini dispersion coefficient
$$ G = \frac \Delta {2 \mu } , $$
where $ \mu $ is the mathematical expectation of the random variable $ X $.
References
| [1] | M.G. Kendall, A. Stuart, "The advanced theory of statistics. Distribution theory" , 3. Design and analysis , Griffin (1969) |
How to Cite This Entry:
Gini average difference. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gini_average_difference&oldid=47098
Gini average difference. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gini_average_difference&oldid=47098
This article was adapted from an original article by K.P. Latyshev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article