shannon (version 0.2.0)

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

Description

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

Usage

rlse_ray(p, alpha)
rlre_ray(p, alpha, delta)
rlhce_ray(p, alpha, delta)
rlae_ray(p, alpha, delta)

Value

The functions rlse_ray, rlre_ray, rlhce_ray, and rlae_ray 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 Rayleigh distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive scale parameter of the Rayleigh distribution (\(\alpha > 0\)).

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

Dey, S., Maiti, S. S., & Ahmad, M. (2016). Comparison of different entropy measures. Pak. J. Statist, 32(2), 97-108.

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_ray

Examples

p <- seq(0.25, 2, by=0.25)
rlse_ray(p, 2)
rlre_ray(p, 2, 0.5)
rlhce_ray(p, 2, 0.5)
rlae_ray(p, 2, 0.5)

# A graphic representation of relative loss (RL)
library(ggplot2)
# p is a truncation time vector
p <- seq(0.25, 2, by = 0.25)
# RL based on the Rényi entropy
z1 <- rlre_ray(p, 0.1, 0.5)
# RL based on the Havrda and Charvat entropy
z2 <- rlhce_ray(p, 0.1, 0.5)
# RL based on the Arimoto entropy
z3 <- rlae_ray(p, 0.1, 0.5)
# RL based on the Shannon entropy
z4 <- rlse_ray(p, 0.1)
df <- data.frame(x = p, RL = z1, z2, z3, z4)
head(df)
p1 <- ggplot(df, aes(x = p, y = RL, color = Entropy))
p1 + geom_line(aes(colour = "RE"), size = 1) + geom_line(aes(x,
    y = z2, colour = "HCE"), size = 1) + geom_line(aes(x, y = z3,
    colour = "AR"), size = 1) + geom_line(aes(x, y = z4, colour = "SE"),
    size = 1) + ggtitle(expression(delta == 0.5 ~ ~alpha == 0.1))