shannon (version 0.2.0)

Rayleigh distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Rayleigh distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Rayleigh distribution.

Usage

se_ray(alpha)
re_ray(alpha, delta)
hce_ray(alpha, delta)
ae_ray(alpha, delta)

Value

The functions se_ray, re_ray, hce_ray, and ae_ray provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Rayleigh distribution and \(\delta\).

Arguments

alpha

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

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 .

Details

The following is the probability density function of the Rayleigh distribution: $$ f(x)=2\alpha xe^{-\alpha x^{2}}, $$ where \(x > 0\) and \(\alpha > 0\).

References

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

Arimoto, S. (1971). Information-theoretical considerations on estimation problems. Inf. Control, 19, 181–194.

See Also

re_exp, re_gamma, re_wei

Examples

se_ray(0.2)
delta <- c(1.5, 2, 3)
re_ray(0.2, delta)
hce_ray(0.2, delta)
ae_ray(0.2, delta)
# A graphic representation of the Rényi entropy (RE)
library(ggplot2)
delta <- c(1.5, 2, 3)
z <- re_ray(0.2, delta)
dat <- data.frame(x = delta , RE = z)
p_re <- ggplot(dat, aes(x = delta, y = RE)) + geom_line()
plot <- p_re + ggtitle(expression(alpha == 0.2))
# A graphic presentation of the Havrda and Charvat entropy (HCE)
delta <- c(1.5, 2, 3)
z <- hce_ray(0.2, delta)
dat <- data.frame(x = delta , HCE = z)
p_hce <- ggplot(dat, aes(x = delta, y = HCE)) + geom_line()
plot <- p_hce + ggtitle(expression(alpha == 0.2))