Rayleigh distribution {shannon} | R Documentation |
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)
Arguments
alpha |
The strictly positive parameter of the Rayleigh distribution ( |
delta |
The strictly positive parameter ( |
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
.
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
.
Author(s)
Muhammad Imran, Christophe Chesneau and Farrukh Jamal
R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.
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
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))