EE: 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 exponentiated exponential distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponentiated exponential distribution.

Usage

se_ee(alpha, beta)
re_ee(alpha, beta, delta)
hce_ee(alpha, beta, delta)
ae_ee(alpha, beta, delta)

Arguments

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

Details

The following is the probability density function of the exponentiated exponential distribution:

f(x)=\alpha\beta e^{-\alpha x}\left(1-e^{-\alpha x}\right)^{\beta-1},

where x > 0, \alpha > 0 and \beta > 0.

Value

The functions se_ee, re_ee, hce_ee, and ae_ee provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponentiated 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. (2011). The exponentiated exponential distribution: a survey. AStA Advances in Statistical Analysis, 95, 219-251.

Gupta, R. D., & Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137(11), 3537-3547.

See Also

re_exp, re_wei, re_nh

Examples

se_ee(0.2, 1.4)
delta <- c(1.5, 2, 3)
re_ee(0.2, 1.4, delta)
hce_ee(0.2, 1.4, delta)
ae_ee(0.2, 1.4, delta)

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