idigamma {joker} | R Documentation |
Inverse Digamma Function
Description
The inverse of the digamma function, i.e. the derivative of the log-gamma function.
Usage
idigamma(x, ...)
Arguments
x |
numeric. The point to evaluate the function. |
... |
extra arguments passed to |
Details
The idigamma()
function implements the inverse of the digamma function
\psi
. It is a numerical approximation based on the Brent optimization
algorithm. Specifically, idigamma()
makes a call to optim()
in order to
solve the equation \psi(x) = y
; more accurately, to find the minimum of
f(x) = \log\Gamma(x) - xy
, whose derivative is
f'(x) = \psi(x) - y
. The optimization is restricted within the tight
bounds derived by Batir (2017). The function is vectorized.
Value
numeric. The evaluated function.
References
Necdet Batir (2017), INEQUALITIES FOR THE INVERSES OF THE POLYGAMMA FUNCTIONS https://arxiv.org/pdf/1705.06547
Oikonomidis, I. & Trevezas, S. (2023), Moment-Type Estimators for the Dirichlet and the Multivariate Gamma Distributions, arXiv, https://arxiv.org/abs/2311.15025
See Also
Examples
idigamma(2)