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

Description

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

Usage

se_f(alpha, beta)
re_f(alpha, beta, delta)
hce_f(alpha, beta, delta)
ae_f(alpha, beta, delta)

Value

The functions se_f, re_f, hce_f, and ae_f provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the F distribution and $\delta$.

Arguments

alpha: The strictly positive parameter (first degree of freedom) of the F distribution ($\alpha > 0$).
beta: The strictly positive parameter (second degree of freedom) of the F 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 F distribution: $$ f(x)=\frac{1}{B(\frac{\alpha}{2},\frac{\beta}{2})}\left(\frac{\alpha}{\beta}\right)^{\frac{\alpha}{2}}x^{\frac{\alpha}{2}-1}\left(1+\frac{\alpha}{\beta}x\right)^{-\left(\frac{\alpha+\beta}{2}\right)}, $$ where $x > 0$, $\alpha > 0$ and $\beta > 0$, and $B(a,b)$ is the standard beta function.

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.

Examples

Run this code

se_f(1.2, 1.4)
delta <- c(2.2, 2.3)
re_f(1.2, 0.4, delta)
hce_f(1.2, 1.4, delta)
ae_f(1.2, 1.4, delta)

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