Normal distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the normal distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the normal distribution.
Usage
se_norm(alpha, beta)
re_norm(alpha, beta, delta)
hce_norm(alpha, beta, delta)
ae_norm(alpha, beta, delta)
Arguments
alpha |
The location parameter of the normal distribution ( |
beta |
The strictly positive scale parameter of the normal distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the normal distribution:
f(x)=\frac{1}{\beta\sqrt{2\pi}}e^{-0.5\left(\frac{x-\alpha}{\beta}\right)^{2}},
where x\in\left(-\infty,+\infty\right)
, \alpha\in\left(-\infty,+\infty\right)
and \beta > 0
. The parameters \alpha
and \beta
represent the mean and standard deviation, respectively.
Value
The functions se_norm, re_norm, hce_norm, and ae_norm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Normal 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
Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.
See Also
Examples
se_norm(0.2, 1.4)
delta <- c(1.5, 2, 3)
re_norm(0.2, 1.4, delta)
hce_norm(0.2, 1.4, delta)
ae_norm(0.2, 1.4, delta)