Beta exponential distribution {shannon} | R Documentation |
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the beta exponential distribution
Description
Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the beta exponential distribution.
Usage
se_bexp(lambda, alpha, beta)
re_bexp(lambda, alpha, beta, delta)
hce_bexp(lambda, alpha, beta, delta)
ae_bexp(lambda, alpha, beta, delta)
Arguments
lambda |
The strictly positive scale parameter of the exponential distribution ( |
alpha |
The strictly positive shape parameter of the beta distribution ( |
beta |
The strictly positive shape parameter of the beta distribution ( |
delta |
The strictly positive parameter ( |
Details
The following is the probability density function of the beta exponential distribution:
f(x)=\frac{\lambda e^{-\beta\lambda x}}{B(\alpha,\beta)}\left(1-e^{-\lambda x}\right)^{\alpha-1},
where x > 0
, \alpha > 0
, \beta > 0
and \lambda > 0
, and B(a,b)
denotes the standard beta function.
Value
The functions se_bexp, re_bexp, hce_bexp, and ae_bexp provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the beta exponential 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., & Kotz, S. (2006). The beta exponential distribution. Reliability Engineering & System Safety, 91(6), 689-697.
See Also
Examples
# Computation of the Shannon entropy
se_bexp(1.2, 0.2, 1.5)
delta <- c(0.2, 0.3, 0.5)
# Computation of the Rényi entropy
re_bexp(1.2, 0.2, 0.5, delta)
# Computation of the Havrda and Charvat entropy
hce_bexp(1.2, 0.2, 1.5, delta)
# Computation of the Arimoto entropy
ae_bexp(1.2, 0.2, 1.5, delta)