Gamma distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the gamma distribution

Description

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

Usage

Se_gamma(alpha, beta)
re_gamma(alpha, beta, delta)
hce_gamma(alpha, beta, delta)
ae_gamma(alpha, beta, delta)

Value

The functions Se_gamma, re_gamma, hce_gamma, and ae_gamma provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the gamma distribution and $\delta$.

Arguments

alpha: The strictly positive shape parameter of the gamma distribution ($\alpha > 0$).
beta: The strictly positive scale parameter of the 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 gamma distribution: $$ f(x)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x}, $$ where $x > 0$, $\alpha > 0$ and $\beta > 0$, and $\Gamma(a)$ is the standard gamma function.

References

Burgin, T. A. (1975). The gamma distribution and inventory control. Journal of the Operational Research Society, 26(3), 507-525.

Examples

Run this code

Se_gamma(1.2, 1.4)
delta <- c(1.5, 2, 3)
re_gamma(1.2, 1.4, delta)
hce_gamma(1.2, 1.4, delta)
ae_gamma(1.2, 1.4, delta)

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