Gamma distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the gamma distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the gamma distribution.
Usage
Se_gamma(alpha, beta)
re_gamma(alpha, beta, delta)
hce_gamma(alpha, beta, delta)
ae_gamma(alpha, beta, delta)
Arguments
alpha |
The strictly positive shape parameter of the gamma distribution ( |
beta |
The strictly positive scale parameter of the gamma distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the gamma distribution:
f(x)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x},
where x > 0
, \alpha > 0
and \beta > 0
, and \Gamma(a)
is the standard gamma function.
Value
The functions Se_gamma, re_gamma, hce_gamma, and ae_gamma provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the gamma 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
Burgin, T. A. (1975). The gamma distribution and inventory control. Journal of the Operational Research Society, 26(3), 507-525.
See Also
Examples
Se_gamma(1.2, 1.4)
delta <- c(1.5, 2, 3)
re_gamma(1.2, 1.4, delta)
hce_gamma(1.2, 1.4, delta)
ae_gamma(1.2, 1.4, delta)