shannon (version 0.2.0)

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

Description

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

Usage

rlse_beta(p, alpha, beta)
rlre_beta(p, alpha, beta, delta)
rlhce_beta(p, alpha, beta, delta)
rlae_beta(p, alpha, beta, delta)

Value

The functions rlse_beta, rlre_beta, rlhce_beta, and rlae_beta 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 beta distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive shape parameter of the beta distribution (\(\alpha > 0\)).

beta

The strictly positive shape parameter of the beta 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

Gupta, A. K., & Nadarajah, S. (2004). Handbook of beta distribution and its applications. CRC Press.

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.

See Also

re_beta

Examples

p <- c(0.25, 0.50, 0.75)
rlse_beta(p, 0.2, 0.4)
rlre_beta(p, 0.2, 0.4, 0.5)
rlhce_beta(p, 0.2, 0.4, 0.5)
rlae_beta(p, 0.2, 0.4, 0.5)