Laplace distribution {shannon} | R Documentation |
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 ( |
beta |
The strictly positive scale parameter of the Laplace distribution ( |
delta |
The strictly positive parameter ( |
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 <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.
References
Cordeiro, G. M., & Lemonte, A. J. (2011). The beta Laplace distribution. Statistics & Probability Letters, 81(8), 973-982.
See Also
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)