Logistic distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the logistic distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the logistic distribution.
Usage
se_logis(mu, sigma)
re_logis(mu, sigma, delta)
hce_logis(mu, sigma, delta)
ae_logis(mu, sigma, delta)
Arguments
mu |
The location parameter of the logistic distribution ( |
sigma |
The strictly positive scale parameter of the logistic distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the logistic distribution:
f(x)=\frac{e^{-\frac{\left(x-\mu\right)}{\sigma}}}{\sigma\left(1+e^{-\frac{\left(x-\mu\right)}{\sigma}}\right)^{2}},
where x\in\left(-\infty,+\infty\right)
, \mu\in\left(-\infty,+\infty\right)
and \sigma > 0
.
Value
The functions se_logis, re_logis, hce_logis, and ae_logis provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the logistic 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
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, Volume 2 (Vol. 289). John Wiley & Sons.
See Also
Examples
se_logis(0.2, 1.4)
delta <- c(2, 3)
re_logis(1.2, 0.4, delta)
hce_logis(1.2, 0.4, delta)
ae_logis(1.2, 0.4, delta)