bexp: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto...

In shannon: Computation of Entropy Measures and Relative Loss

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 (\lambda > 0).
alpha	The strictly positive shape parameter of the beta distribution (\alpha > 0).
beta	The strictly positive shape parameter of the beta distribution (\beta > 0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

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 <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal [e-mail].

References

Nadarajah, S., & Kotz, S. (2006). The beta exponential distribution. Reliability Engineering & System Safety, 91(6), 689-697.

See Also

re_beta, re_exp

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)

shannon documentation built on Sept. 11, 2024, 7:48 p.m.