shannon (version 0.2.0)

Truncated Chi-squared distribution: Relative loss for various entropy measures using the truncated Chi-squared distribution

Description

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

Usage

rlse_chi(p, n)
rlre_chi(p, n, delta)
rlhce_chi(p, n, delta)
rlae_chi(p, n, delta)

Value

The functions rlse_chi, rlre_chi, rlhce_chi, and rlae_chi 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 Chi-squared distribution, \(p\) and \(\delta\).

Arguments

n

The degree of freedom and positive parameter of the Chi-squared distribution (\(n > 0\)).

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_chi

Examples

p <- c(1, 1.7, 3)
rlse_chi(p, 2)
rlre_chi(p, 2, 0.5)
rlhce_chi(p, 2, 0.5)
rlae_chi(p, 2, 0.5)