gomp: 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 Gompertz distribution

Description

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

Usage

se_gomp(alpha, beta)
re_gomp(alpha, beta, delta)
hce_gomp(alpha, beta, delta)
ae_gomp(alpha, beta, delta)

Arguments

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

Details

The following is the probability density function of the Gompertz distribution:

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

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

Value

The functions se_gomp, re_gomp, hce_gomp, and ae_gomp provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Gompertz 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

Soliman, A. A., Abd-Ellah, A. H., Abou-Elheggag, N. A., & Abd-Elmougod, G. A. (2012). Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data. Computational Statistics & Data Analysis, 56(8), 2471-2485.

See Also

re_exp, re_gamma, re_ray

Examples

se_gomp(2.4,0.2)
delta <- c(2, 3)
re_gomp(2.4,0.2, delta)
hce_gomp(2.4,0.2, delta)
ae_gomp(2.4,0.2, delta)

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