shannon (version 0.2.0)

Truncated inverse-gamma distribution: Relative loss for various entropy measures using the truncated inverse-gamma distribution

Description

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

Usage

rlse_ig(p, alpha, beta)
rlre_ig(p, alpha, beta, delta)
rlhce_ig(p, alpha, beta, delta)
rlae_ig(p, alpha, beta, delta)

Value

The functions rlse_ig, rlre_ig, rlhce_ig, and rlae_ig 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 inverse-gamma distribution, \(p\) 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 (\(\beta > 0\)).

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.

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.

See Also

re_ig

Examples

p <- c(1.25, 1.50)
rlse_ig(p, 1.2, 0.2)
rlre_ig(p, 1.2, 0.2, 0.5)
rlhce_ig(p, 1.2, 0.2, 0.5)
rlae_ig(p, 1.2, 0.2, 0.5)