Weibull distribution {shannon} | R Documentation |
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)
Arguments
alpha |
The strictly positive scale parameter of the Weibull distribution ( |
beta |
The strictly positive shape parameter of the Weibull distribution ( |
delta |
The strictly positive parameter ( |
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
.
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
.
Author(s)
Muhammad Imran, Christophe Chesneau and Farrukh Jamal
R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.
References
Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics, 18, 293-297.
See Also
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)