f: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto...

In shannon: Computation of Entropy Measures and Relative Loss

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)

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).

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.

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.

Author(s)

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal [e-mail].

References

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

See Also

re_exp, re_gamma

Examples

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)

shannon documentation built on Sept. 11, 2024, 7:48 p.m.