shannon (version 0.2.0)

Burr XII distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Burr XII distribution

Description

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

Usage

se_burr(k, c)
re_burr(k, c, delta)
hce_burr(k, c, delta)
ae_burr(k, c, delta)

Value

The functions se_burr, re_burr, hce_burr, and ae_burr provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Burr XII distribution and \(\delta\).

Arguments

k

The strictly positive shape parameter of the Burr XII distribution (\(k > 0\)).

c

The strictly positive shape parameter of the Burr XII distribution (\(c > 0\)).

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 Burr XII distribution: $$ f(x)=kcx^{c-1}\left(1+x^{c}\right)^{-k-1}, $$ where \(x > 0\), \(c > 0\) and \(k > 0\).

References

Rodriguez, R. N. (1977). A guide to the Burr type XII distributions. Biometrika, 64(1), 129-134.

Zimmer, W. J., Keats, J. B., & Wang, F. K. (1998). The Burr XII distribution in reliability analysis. Journal of Quality Technology, 30(4), 386-394.

See Also

re_gamma, re_wei

Examples

se_burr(0.2, 1.4)
delta <- c(2, 3)
re_burr(1.2, 1.4, delta)
hce_burr(1.2, 1.4, delta)
ae_burr(1.2, 1.4, delta)