shannon (version 0.2.0)

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

Description

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

Usage

se_wei(alpha, beta)
re_wei(alpha, beta, delta)
hce_wei(alpha, beta, delta)
ae_wei(alpha, beta, delta)

Value

The functions se_wei, re_wei, hce_wei, and ae_wei provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Weibull distribution and \(\delta\).

Arguments

alpha

The strictly positive scale parameter of the Weibull distribution (\(\alpha > 0\)).

beta

The strictly positive shape parameter of the Weibull 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 Weibull distribution: $$ f(x)=\frac{\beta}{\alpha}\left(\frac{x}{\alpha}\right)^{\beta-1}e^{-(\frac{x}{\alpha})^{\beta}}, $$ where \(x > 0\), \(\alpha > 0\) and \(\beta > 0\).

References

Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics, 18, 293-297.

See Also

re_exp, re_gamma, re_ee

Examples

se_wei(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_wei(1.2, 0.2, delta)
hce_wei(1.2, 0.2, delta)
ae_wei(1.2, 0.2, delta)