shannon (version 0.2.0)

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

Description

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

Usage

se_lom(alpha, beta)
re_lom(alpha, beta, delta)
hce_lom(alpha, beta, delta)
ae_lom(alpha, beta, delta)

Value

The functions se_lom, re_lom, hce_lom, and ae_lom provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Lomax distribution and \(\delta\).

Arguments

alpha

The strictly positive shape parameter of the Lomax distribution (\(\alpha > 0\)).

beta

The strictly positive scale parameter of the Lomax distribution (\(\beta > 0\)).

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 Lomax distribution: $$ f(x)=\frac{\alpha}{\beta}\left(1+\frac{x}{\beta}\right)^{-\alpha-1}, $$ where \(x > 0\), \(\alpha > 0\) and \(\beta > 0\).

References

Abd-Elfattah, A. M., Alaboud, F. M., & Alharby, A. H. (2007). On sample size estimation for Lomax distribution. Australian Journal of Basic and Applied Sciences, 1(4), 373-378.

See Also

re_exp, re_gamma

Examples

se_lom(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_lom(1.2, 0.2, delta)
hce_lom(1.2, 0.2, delta)
ae_lom(1.2, 0.2, delta)