Gumbel distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Gumbel distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Gumbel distribution.
Usage
Se_gum(alpha, beta)
re_gum(alpha, beta, delta)
hce_gum(alpha, beta, delta)
ae_gum(alpha, beta, delta)
Arguments
alpha |
The location parameter of the Gumbel distribution ( |
beta |
The strictly positive scale parameter of the Gumbel distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the Gumbel distribution:
f(x)=\frac{1}{\beta}e^{-(z+e^{-z})},
where z=\frac{x-\alpha}{\beta}
, x\in\left(-\infty,+\infty\right)
, \alpha\in\left(-\infty,+\infty\right)
and \beta > 0
.
Value
The functions Se_gum, re_gum, hce_gum, and ae_gum provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Gumbel 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
Gomez, Y. M., Bolfarine, H., & Gomez, H. W. (2019). Gumbel distribution with heavy tails and applications to environmental data. Mathematics and Computers in Simulation, 157, 115-129.
See Also
Examples
Se_gum(1.2, 1.4)
delta <- c(2, 3)
re_gum(1.2, 0.4, delta)
hce_gum(1.2, 0.4, delta)
ae_gum(1.2, 0.4, delta)