lnorm: 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 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)

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).

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.

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.

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

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)

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