Description Usage Arguments Details Value See Also
If X ~ InvRootGamma(scale=sigma.sq, df=nu), then 1/(X^2) ~ Gamma(shape=nu/2, rate=nu*sigma.sq/2).
1 2 3 4 5 | dinvrootgamma(x, shape, df, log = FALSE)
rinvrootgamma(n, shape, df)
pinvrootgamma(q, shape, df, log = FALSE)
|
x |
vector of quantiles |
shape |
parameter, where shape>0 |
df |
degrees of freedom parameter, where df>0 |
log |
logical; if TRUE, probabilities p are given as log(p). |
n |
number of random deviates to draw |
q |
vector of quantiles |
The density function of the inverse-root-gamma distribution shape σ^2 and ν degrees of freedom is
p(θ) = I(θ>0)\frac{2}{Γ≤ft(\frac{ν}{2}\right)} ≤ft( \frac{νσ^2}{2}\right)^{ν/2}\frac{1}{θ^{ν+1}} \exp≤ft\{-\frac{ν σ^2}{2θ^2}\right\}.
The cdf is
P(x) = \frac{Γ ≤ft(\frac{ν }{2},\frac{ν σ ^2}{2 x^2}\right)}{Γ ≤ft(\frac{ν }{2}\right)}.
Note that some authors use alternative parameterizations; see especially dinvgamma.
'dinvgamma' gives the density and 'rinvgamma' generates random deviates.
Other gamma: dinvgamma
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