Gamma distribution | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the gamma distribution.
Se_gamma(alpha, beta)
re_gamma(alpha, beta, delta)
hce_gamma(alpha, beta, delta)
ae_gamma(alpha, beta, delta)
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 ( |
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.
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
.
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.
Burgin, T. A. (1975). The gamma distribution and inventory control. Journal of the Operational Research Society, 26(3), 507-525.
re_exp, re_wei
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)
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