risk_norm: Relative loss for various entropy measures using the...

In shannon: Computation of Entropy Measures and Relative Loss

Relative loss for various entropy measures using the truncated normal distribution

Description

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

Usage

rlse_norm(p, alpha, beta)
rlre_norm(p, alpha, beta, delta)
rlhce_norm(p, alpha, beta, delta)
rlae_norm(p, alpha, beta, delta)

Arguments

alpha	The location parameter of the normal distribution (\alpha\in\left(-\infty,+\infty\right)).
beta	The strictly positive scale parameter of the normal distribution (\beta > 0).
p	The truncation time (p>0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Value

The functions rlse_norm, rlre_norm, rlhce_norm, and rlae_norm 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 normal distribution, p 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

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.

Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.

See Also

re_norm

Examples

p <- c(0.25, 0.50, 0.75)
rlse_norm(p, 0.2, 1)
rlre_norm(p, 0.2, 1, 0.5)
rlhce_norm(p, 0.2, 1, 0.5)
rlae_norm(p, 0.2, 1, 0.5)

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