Exponentiated Weibull distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponentiated Weibull distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponentiated Weibull distribution.
Usage
se_ew(a, beta, zeta)
re_ew(a, beta, zeta, delta)
hce_ew(a, beta, zeta, delta)
ae_ew(a, beta, zeta, delta)
Arguments
a |
The strictly positive shape parameter of the exponentiated Weibull distribution ( |
beta |
The strictly positive scale parameter of the baseline Weibull distribution ( |
zeta |
The strictly positive shape parameter of the baseline Weibull distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the exponentiated Weibull distribution:
f(x)=a\zeta\beta^{-\zeta}x^{\zeta-1}e^{-\left(\frac{x}{\beta}\right)^{\zeta}}\left[1-e^{-\left(\frac{x}{\beta}\right)^{\zeta}}\right]^{a-1},
where x > 0
, a > 0
, \beta > 0
and \zeta > 0
.
Value
The functions se_ew, re_ew, hce_ew, and ae_ew provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponentiated 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
Nadarajah, S., Cordeiro, G. M., & Ortega, E. M. (2013). The exponentiated Weibull distribution: a survey. Statistical Papers, 54, 839-877.
See Also
Examples
se_ew(0.8, 0.2, 0.8)
delta <- c(1.5, 2, 3)
re_ew(1.2, 1.2, 1.4, delta)
hce_ew(1.2, 1.2, 1.4, delta)
ae_ew(1.2, 1.2, 1.4, delta)