Birnbaum-Saunders distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Birnbaum-Saunders distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Birnbaum-Saunders distribution.
Usage
se_bs(v)
re_bs(v, delta)
hce_bs(v, delta)
ae_bs(v, delta)
Arguments
v |
The strictly positive scale parameter of the Birnbaum-Saunders distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the Birnbaum-Saunders distribution:
f(x)=\frac{x^{0.5}+x^{-0.5}}{2vx}\phi\left(\frac{x^{0.5}-x^{-0.5}}{v}\right),
where x > 0
and v > 0
, and \phi(x)
is the probability density function of the standard normal distribution.
Value
The functions se_bs, re_bs, hce_bs, and ae_bs provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Birnbaum-Saunders 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
Chan, S., Nadarajah, S., & Afuecheta, E. (2016). An R package for value at risk and expected shortfall. Communications in Statistics Simulation and Computation, 45(9), 3416-3434.
Arimoto, S. (1971). Information-theoretical considerations on estimation problems. Inf. Control, 19, 181–194.
See Also
Examples
se_bs(0.2)
delta <- c(1.5, 2, 3)
re_bs(0.2, delta)
hce_bs(0.2, delta)
ae_bs(0.2, delta)