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

In shannon: Computation of Entropy Measures and Relative Loss

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the inverse-gamma distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the inverse-gamma distribution.

Usage

se_ig(alpha, beta)
re_ig(alpha, beta, delta)
hce_ig(alpha, beta, delta)
ae_ig(alpha, beta, delta)

Arguments

alpha	The strictly positive shape parameter of the inverse-gamma distribution (\alpha > 0).
beta	The strictly positive scale parameter of the inverse-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 inverse-gamma distribution:

f(x)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\frac{\beta}{x}},

where x > 0, \alpha > 0 and \beta > 0, and \Gamma(a) is the standard gamma function.

Value

The functions se_ig, re_ig, hce_ig, and ae_ig provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the inverse-gamma distribution and \delta.

Author(s)

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal [e-mail].

References

Rivera, P. A., Calderín-Ojeda, E., Gallardo, D. I., & Gómez, H. W. (2021). A compound class of the inverse Gamma and power series distributions. Symmetry, 13(8), 1328.

Glen, A. G. (2017). On the inverse gamma as a survival distribution. Computational Probability Applications, 15-30.

See Also

re_exp, re_gamma

Examples

se_ig(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_ig(1.2, 0.2, delta)
hce_ig(1.2, 0.2, delta)
ae_ig(1.2, 0.2, delta)

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