Kumaraswamy normal distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Kumaraswamy normal distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Kumaraswamy normal distribution.
Usage
se_kumnorm(mu, sigma, a, b)
re_kumnorm(mu, sigma, a, b, delta)
hce_kumnorm(mu, sigma, a, b, delta)
ae_kumnorm(mu, sigma, a, b, delta)
Arguments
mu |
The location parameter of the normal distribution ( |
sigma |
The strictly positive scale parameter of the normal distribution ( |
a |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
b |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the Kumaraswamy normal distribution:
f(x)=\frac{ab}{\sigma}\phi\left(\frac{x-\mu}{\sigma}\right)\left[\Phi\left(\frac{x-\mu}{\sigma}\right)\right]^{a-1}\left[1-\Phi\left(\frac{x-\mu}{\sigma}\right)^{a}\right]^{b-1},
where x\in\left(-\infty,+\infty\right)
, \mu\in\left(-\infty,+\infty\right)
, \sigma > 0
, a > 0
and b > 0
, and the functions \phi(t)
and \Phi(t)
, denote the probability density function and cumulative distribution function of the standard normal distribution, respectively.
Value
The functions se_kumnorm, re_kumnorm, hce_kumnorm, and ae_kumnorm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Kumaraswamy normal 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
Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.
See Also
Examples
se_kumnorm(0.2, 1.5, 1, 1)
delta <- c(1.5, 2, 3)
re_kumnorm(1.2, 1, 2, 1.5, delta)
hce_kumnorm(1.2, 1, 2, 1.5, delta)
ae_kumnorm(1.2, 1, 2, 1.5, delta)