Exponential extension distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponential extension distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponential extension distribution.
Usage
se_nh(alpha, beta)
re_nh(alpha, beta, delta)
hce_nh(alpha, beta, delta)
ae_nh(alpha, beta, delta)
Arguments
alpha |
The strictly positive parameter of the exponential extension distribution ( |
beta |
The strictly positive parameter of the exponential extension distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the exponential extension distribution:
f(x)=\alpha\beta(1+\alpha x)^{\beta-1}e^{1-(1+\alpha x)^{\beta}},
where x > 0
, \alpha > 0
and \beta > 0
.
Value
The functions se_nh, re_nh, hce_nh, and ae_nh provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponential extension 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., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558.
See Also
re_exp, re_gamma, re_ee, re_wei
Examples
se_nh(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_nh(1.2, 0.2, delta)
hce_nh(1.2, 0.2, delta)
ae_nh(1.2, 0.2, delta)