shannon (version 0.2.0)

Log-normal distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the log-normal distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the log-normal distribution.

Usage

se_lnorm(mu, sigma)
re_lnorm(mu, sigma, delta)
hce_lnorm(mu, sigma, delta)
ae_lnorm(mu, sigma, delta)

Value

The functions se_lnorm, re_lnorm, hce_lnorm, and ae_lnorm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the log-normal distribution and \(\delta\).

Arguments

mu

The location parameter (\(\mu\in\left(-\infty,+\infty\right)\)).

sigma

The strictly positive scale parameter of the log-normal 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 log-normal distribution: $$ f(x)=\frac{1}{x\sigma\sqrt{2\pi}}e^{-\frac{\left(\log(x)-\mu\right)^{2}}{2\sigma^{2}}}, $$ where \(x > 0\), \(\mu\in\left(-\infty,+\infty\right)\) and \(\sigma > 0\).

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, Volume 1, Chapter 14. Wiley, New York.

See Also

re_wei, re_norm

Examples

se_lnorm(0.2, 1.4)
delta <- c(2, 3)
re_lnorm(1.2, 0.4, delta)
hce_lnorm(1.2, 0.4, delta)
ae_lnorm(1.2, 0.4, delta)