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Intuitive Parameterization of the Bivariate Normal Distribution
This Demonstration shows a parameterization of a bivariate normal distribution by specifying an angle of cross-correlation
. The controls
and
are the
and
spreads of the blob.
Contributed by:
Robert L. Brown
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A bivariate normal distribution can be represented by three polar variables:
,
,
or with the parameters
,
,
, where
,
,
.
.
Conversely, define:
,
,
.
Then this gives
,
,
from
,
,
:
,
,
.
See the Wikipedia article
Gaussian function
.
RELATED LINKS
Bivariate Normal Distribution
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Intuitive Parameterization of the Bivariate Normal Distribution
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/IntuitiveParameterizationOfTheBivariateNormalDistribution/
Contributed by:
Robert L. Brown
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