gamma: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto...

Gamma distributionR 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 (\alpha > 0).

beta

The strictly positive scale parameter of the gamma distribution (\beta > 0).

delta

The strictly positive parameter (\delta > 0) and (\delta \ne 1).

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

re_exp, re_wei

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)

shannon documentation built on Sept. 11, 2024, 7:48 p.m.