kexp: Compute the Rényi, Havrda and Charvat, and Arimoto entropies...

In shannon: Computation of Entropy Measures and Relative Loss

Compute the Rényi, Havrda and Charvat, and Arimoto entropies of the Kumaraswamy exponential distribution

Description

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

Usage

re_kexp(lambda, a, b, delta)
hce_kexp(lambda, a, b, delta)
ae_kexp(lambda, a, b, delta)

Arguments

a	The strictly positive shape parameter of the Kumaraswamy distribution (a > 0).
b	The strictly positive shape parameter of the Kumaraswamy distribution (b > 0).
lambda	The strictly positive parameter of the exponential distribution (\lambda > 0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Details

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

f(x)=ab\lambda e^{-\lambda x}\left(1-e^{-\lambda x}\right)^{a-1}\left\{ 1-\left(1-e^{-\lambda x}\right)^{a}\right\} ^{b-1},

where x > 0, a > 0, b > 0 and \lambda > 0.

Value

The functions re_kexp, hce_kexp, and ae_kexp provide the Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Kumaraswamy 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

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

re_exp, re_kum

Examples

delta <- c(1.5, 2, 3)
re_kexp(1.2, 1.2, 1.4, delta)
hce_kexp(1.2, 1.2, 1.4, delta)
ae_kexp(1.2, 1.2, 1.4, delta)

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