shannon (version 0.2.0)

Logistic distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the logistic distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the logistic distribution.

Usage

se_logis(mu, sigma)
re_logis(mu, sigma, delta)
hce_logis(mu, sigma, delta)
ae_logis(mu, sigma, delta)

Value

The functions se_logis, re_logis, hce_logis, and ae_logis provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the logistic distribution and \(\delta\).

Arguments

mu

The location parameter of the logistic distribution (\(\mu\in\left(-\infty,+\infty\right)\)).

sigma

The strictly positive scale parameter of the logistic distribution (\(\sigma > 0\)).

delta

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

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

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

Details

The following is the probability density function of the logistic distribution: $$ f(x)=\frac{e^{-\frac{\left(x-\mu\right)}{\sigma}}}{\sigma\left(1+e^{-\frac{\left(x-\mu\right)}{\sigma}}\right)^{2}}, $$ where \(x\in\left(-\infty,+\infty\right)\), \(\mu\in\left(-\infty,+\infty\right)\) and \(\sigma > 0\).

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, Volume 2 (Vol. 289). John Wiley & Sons.

See Also

re_gum, re_norm

Examples

se_logis(0.2, 1.4)
delta <- c(2, 3)
re_logis(1.2, 0.4, delta)
hce_logis(1.2, 0.4, delta)
ae_logis(1.2, 0.4, delta)