joker (version 0.14.2)

idigamma: Inverse Digamma Function

Description

The inverse of the digamma function, i.e. the derivative of the log-gamma function.

Usage

idigamma(x, ...)

Value

numeric. The evaluated function.

Arguments

x

numeric. The point to evaluate the function.

...

extra arguments passed to optim().

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.

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

optim()

Examples

# \donttest{
idigamma(2)
# }