shannon (version 0.2.0)

Truncated Laplace distribution: Relative loss for various entropy measures using the truncated Laplace distribution

Description

Compute the relative information loss of the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the truncated Laplace distribution.

Usage

rlse_lap(p, alpha, beta)
rlre_lap(p, alpha, beta, delta)
rlhce_lap(p, alpha, beta, delta)
rlae_lap(p, alpha, beta, delta)

Value

The functions rlse_lap, rlre_lap, rlhce_lap, and rlae_lap provide the relative information loss based on the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the truncated Laplace distribution, \(p\) and \(\delta\).

Arguments

alpha

Location parameter of the Laplace distribution (\(\alpha\in\left(-\infty,+\infty\right)\)).

beta

The strictly positive scale parameter of the Laplace distribution (\(\beta > 0\)).

p

The truncation time \((p>0)\).

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 .

References

Awad, A. M., & Alawneh, A. J. (1987). Application of entropy to a life-time model. IMA Journal of Mathematical Control and Information, 4(2), 143-148.

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

See Also

re_lap

Examples

p <- c(0.25, 0.50, 0.75)
rlse_lap(p, 0.2, 0.4)
rlre_lap(p, 0.2, 0.4, 0.5)
rlhce_lap(p, 0.2, 0.4, 0.5)
rlae_lap(p, 0.2, 0.4, 0.5)