fre: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto...

In shannon: Computation of Entropy Measures and Relative Loss

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Fréchet distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Fréchet distribution.

Usage

se_fre(alpha, beta, zeta)
re_fre(alpha, beta, zeta, delta)
hce_fre(alpha, beta, zeta, delta)
ae_fre(alpha, beta, zeta, delta)

Arguments

alpha	The parameter of the Fréchet distribution (\alpha>0).
beta	The parameter of the Fréchet distribution (\beta\in\left(-\infty,+\infty\right)).
zeta	The parameter of the Fréchet distribution (\zeta>0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Details

The following is the probability density function of the Fréchet distribution:

f(x)=\frac{\alpha}{\zeta}\left(\frac{x-\beta}{\zeta}\right)^{-1-\alpha}e^{-(\frac{x-\beta}{\zeta})^{-\alpha},}

where x>\beta, \alpha>0, \zeta>0 and \beta\in\left(-\infty,+\infty\right). The Fréchet distribution is also known as inverse Weibull distribution and special case of the generalized extreme value distribution.

Value

The functions se_fre, re_fre, hce_fre, and ae_fre provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Fréchet distribution distribution and \delta.

Author(s)

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal [e-mail].

References

Abbas, K., & Tang, Y. (2015). Analysis of Fréchet distribution using reference priors. Communications in Statistics-Theory and Methods, 44(14), 2945-2956.

See Also

re_exp, re_gum

Examples

se_fre(0.2, 1.4, 1.2)
delta <- c(2, 3)
re_fre(1.2, 0.4, 1.2, delta)
hce_fre(1.2, 0.4, 1.2, delta)
ae_fre(1.2, 0.4, 1.2, delta)

shannon documentation built on Sept. 11, 2024, 7:48 p.m.