shannon (version 0.2.0)

Birnbaum-Saunders distribution: 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)

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 \(\delta\).

Arguments

v

The strictly positive scale parameter of the Birnbaum-Saunders distribution (\(v > 0\)).

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 .

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.

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

re_exp, re_chi

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)