Gompertz distribution {shannon} | R Documentation |
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 ( |
beta |
The strictly positive parameter of the Gompertz distribution ( |
delta |
The strictly positive parameter ( |
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 <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.
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
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)