Download inverse Gamma distribution

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inverse Gamma distribution
Inverse-gamma distribution
Inverse-gamma
Probability density function
Cumulative distribution function
parameters:
support:
pdf:
cdf:
mean:
mode:
variance:
skewness:
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ex.kurtosis:
entropy:
mgf:
cf: shape (real)scale (real)for for for for
In probability theory and statistics, the inverse gamma distribution is a
two-parameter family of continuous probability distributions on the positive real
line, which is the distribution of the reciprocal of a variable distributed according
to the gamma distribution. Perhaps the chief use of the inverse gamma distribution
is in Bayesian statistics, where it serves as the conjugate prior of the variance
of a normal distribution. However, it is common
among Bayesians to consider an alternative parametrization of the normal distribution
in
terms
of
the
precision,defined
as
the
reciprocal
of
http://www.wenkuxiazai.com/doc/e495348bcc22bcd126ff0c86.htmlwhich
the
variance,
allows
the
gamma distribution to be used directly as a conjugateprior.Characterization
Probability density function
The inverse gamma distribution's probability density function is defined over the
support
with shape parameter and scale parameter .
Cumulative distribution function
The cumulative distribution function is the regularized gamma function
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where the numerator is the upper incomplete gamma function and the denominator is
the gamma function. Manymath packages allow you to compute Q, the regularized gamma
function, directly.
Properties
It is possible to show that for
and
where is the digamma function.
Related distributions
?If
?If
?If
?If then then then (Gamma distribution) then
(inverse-chi-squared
(Lévy
distribution)(scaled-inverse-chi-squared
distribution)?If
distributhttp://www.wenkuxiazai.com/doc/e495348bcc22bcd126ff0c86.htmlion)
then
?Inverse gamma distribution is a special case of type 5 Pearson distribution
?A
multivariate
generalization
of
the
inverse-gamma
distribution
is
the
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inverse-Wishart distribution.
Derivation from Gamma distribution
The pdf of the gamma distribution is
and define the transformation
then the resulting transformation is
Replacing with ; with ; and with
results in the inverse-gamma pdf shown above
Article Sources and Contributors
Inverse-gamma
distribution
Source:
http://en.wikipedia.org/w/index.php?oldid=456392677
Contributors:
Benwing,
Biostatprof, Btyner, Cburnett, Cquike, Dstivers, Fnielsen, Giftlite,Iwaterpolo,
Josevellezcaldas, Kastchei, M27315, MarkSweep, Melcombe, MisterSheik, PAR, Qwfp,
[email protected],
Rlendog,
Rphlypo,
Sheppa28,
Slavatrudu,
Tomi,
User
A1,
28anonymous edits
Image
Sources,
Licenses
and
Contributhttp://www.wenkuxiazai.com/doc/e495348bcc22bcd126ff0c86.htmlors
Image:Inverse
gamma
pdf.png
http://en.wikipedia.org/w/index.php?title=File:Inverse_gamma_pdf.png
GNU General Public License
cdf.png
Source:
License:
Contributors: Alejo2083, CburnettImage:Inverse gamma
Source:
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http://en.wikipedia.org/w/index.php?title=File:Inverse_gamma_cdf.png
GNU General Public License
License:
Contributors: Alejo2083, CburnettLicense
Creative Commons Attribution-Share Alike 3.0 Unported
//creativecommons.org/licenses/by-sa/3.0/
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