lap: 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 Laplace or the double exponential distributiondistribution

Description

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

Usage

Se_lap(alpha, beta)
re_lap(alpha, beta, delta)
hce_lap(alpha, beta, delta)
ae_lap(alpha, beta, delta)

Arguments

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

Details

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

f(x)=\frac{1}{2\beta}e^{\frac{-|x-\alpha|}{\beta}},

where x\in\left(-\infty,+\infty\right), \alpha\in\left(-\infty,+\infty\right) and \beta > 0.

Value

The functions Se_lap, re_lap, hce_lap, and ae_lap provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Laplace 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

Cordeiro, G. M., & Lemonte, A. J. (2011). The beta Laplace distribution. Statistics & Probability Letters, 81(8), 973-982.

See Also

re_gum, re_norm

Examples

Se_lap(0.2, 1.4)
delta <- c(2, 3)
re_lap(1.2, 0.4, delta)
hce_lap(1.2, 0.4, delta)
ae_lap(1.2, 0.4, delta)

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