norm: 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 normal distribution

Description

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

Usage

se_norm(alpha, beta)
re_norm(alpha, beta, delta)
hce_norm(alpha, beta, delta)
ae_norm(alpha, beta, delta)

Arguments

alpha	The location parameter of the normal distribution (\alpha\in\left(-\infty,+\infty\right)).
beta	The strictly positive scale parameter of the normal distribution (\beta > 0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Details

The following is the probability density function of the normal distribution:

f(x)=\frac{1}{\beta\sqrt{2\pi}}e^{-0.5\left(\frac{x-\alpha}{\beta}\right)^{2}},

where x\in\left(-\infty,+\infty\right), \alpha\in\left(-\infty,+\infty\right) and \beta > 0. The parameters \alpha and \beta represent the mean and standard deviation, respectively.

Value

The functions se_norm, re_norm, hce_norm, and ae_norm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the 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

Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.

See Also

re_gum

Examples

se_norm(0.2, 1.4)
delta <- c(1.5, 2, 3)
re_norm(0.2, 1.4, delta)
hce_norm(0.2, 1.4, delta)
ae_norm(0.2, 1.4, delta)

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