shannon (version 0.2.0)

Truncated F distribution: Relative loss for various entropy measures using the truncated F distribution

Description

Compute the relative information loss of the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the truncated F distribution.

Usage

rlse_f(p, alpha, beta)
rlre_f(p, alpha, beta, delta)
rlhce_f(p, alpha, beta, delta)
rlae_f(p, alpha, beta, delta)

Value

The functions rlse_f, rlre_f, rlhce_f, and rlae_f provide the relative information loss based on the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the truncated F distribution, \(p\) 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 (\(\beta > 0\)).

p

The truncation time \((p>0)\).

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 <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal .

References

Awad, A. M., & Alawneh, A. J. (1987). Application of entropy to a life-time model. IMA Journal of Mathematical Control and Information, 4(2), 143-148. Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.

See Also

re_f

Examples

p <- c(1.25, 1.50, 1.75)
rlse_f(p, 4, 6)
rlre_f(p, 4, 6, 0.5)
rlhce_f(p, 4, 6, 0.5)
rlae_f(p, 4, 6, 0.5)