Nakagami distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Nakagami distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Nakagami distribution.
Usage
se_naka(alpha, beta)
re_naka(alpha, beta, delta)
hce_naka(alpha, beta, delta)
ae_naka(alpha, beta, delta)
Arguments
alpha |
The strictly positive scale parameter of the Nakagami distribution ( |
beta |
The strictly positive shape parameter of the Nakagami distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the Nakagami distribution:
f(x)=\frac{2\alpha^{\alpha}}{\Gamma(\alpha)\beta^{\alpha}}x^{2\alpha-1}e^{-\frac{\alpha x^{2}}{\beta}},
where x > 0
, \alpha > 0
and \beta > 0
, and \Gamma(a)
is the standard gamma function.
Value
The functions se_naka, re_naka, hce_naka, and ae_naka provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Nakagami 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
Schwartz, J., Godwin, R. T., & Giles, D. E. (2013). Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution. Journal of Statistical Computation and Simulation, 83(3), 434-445.
See Also
Examples
se_naka(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_naka(1.2, 0.2, delta)
hce_naka(1.2, 0.2, delta)
ae_naka(1.2, 0.2, delta)