shannon (version 0.2.0)

Truncated Gompertz distribution: Relative loss for various entropy measures using the truncated Gompertz distribution

Description

Compute the relative information loss of the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the truncated Gompertz distribution.

Usage

rlse_gomp(p, alpha, beta)
rlre_gomp(p, alpha, beta, delta)
rlhce_gomp(p, alpha, beta, delta)
rlae_gomp(p, alpha, beta, delta)

Value

The functions rlse_gomp, rlre_gomp, rlhce_gomp, and rlae_gomp provide the relative information loss based on the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the truncated Gompertz distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive parameter of the Gompertz distribution (\(\alpha > 0\)).

beta

The strictly positive parameter of the Gompertz distribution (\(\beta > 0\)).

p

The truncation time \((p>0)\).

delta

The strictly positive parameter (\(\delta > 0\)) and (\(\delta \ne 1\)).

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal .

References

Awad, A. M., & Alawneh, A. J. (1987). Application of entropy to a life-time model. IMA Journal of Mathematical Control and Information, 4(2), 143-148.

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_gomp

Examples

p <- c(0.25, 0.50)
rlse_gomp(p, 2.4,0.2)
rlre_gomp(p, 2.4,0.2, 0.5)
rlhce_gomp(p, 2.4,0.2, 0.5)
rlae_gomp(p, 2.4,0.2, 0.5)