Inverse-gamma distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the inverse-gamma distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the inverse-gamma distribution.

Usage

se_ig(alpha, beta)
re_ig(alpha, beta, delta)
hce_ig(alpha, beta, delta)
ae_ig(alpha, beta, delta)

Value

The functions se_ig, re_ig, hce_ig, and ae_ig provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the inverse-gamma distribution and $\delta$.

Arguments

alpha: The strictly positive shape parameter of the inverse-gamma distribution ($\alpha > 0$).
beta: The strictly positive scale parameter of the inverse-gamma distribution ($\beta > 0$).
delta: The strictly positive parameter ($\delta > 0$) and ($\delta \ne 1$).

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.

Details

The following is the probability density function of the inverse-gamma distribution: $$ f(x)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\frac{\beta}{x}}, $$ where $x > 0$, $\alpha > 0$ and $\beta > 0$, and $\Gamma(a)$ is the standard gamma function.

References

Rivera, P. A., Calderín-Ojeda, E., Gallardo, D. I., & Gómez, H. W. (2021). A compound class of the inverse Gamma and power series distributions. Symmetry, 13(8), 1328.

Glen, A. G. (2017). On the inverse gamma as a survival distribution. Computational Probability Applications, 15-30.

Examples

Run this code

se_ig(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_ig(1.2, 0.2, delta)
hce_ig(1.2, 0.2, delta)
ae_ig(1.2, 0.2, delta)

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