Laplace distribution: 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)

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 $\delta$.

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 ($\delta \ne 1$).

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.

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 $\beta > 0$.

References

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

Examples

Run this code

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)

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