Nakagami distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Nakagami distribution

Description

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

Usage

se_naka(alpha, beta)
re_naka(alpha, beta, delta)
hce_naka(alpha, beta, delta)
ae_naka(alpha, beta, delta)

Value

The functions se_naka, re_naka, hce_naka, and ae_naka provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Nakagami distribution and $\delta$.

Arguments

alpha: The strictly positive scale parameter of the Nakagami distribution ($\alpha > 0$).
beta: The strictly positive shape parameter of the Nakagami distribution ($\beta > 0$).
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 <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.

Details

The following is the probability density function of the Nakagami distribution: $$ f(x)=\frac{2\alpha^{\alpha}}{\Gamma(\alpha)\beta^{\alpha}}x^{2\alpha-1}e^{-\frac{\alpha x^{2}}{\beta}}, $$ where $x > 0$, $\alpha > 0$ and $\beta > 0$, and $\Gamma(a)$ is the standard gamma function.

References

Schwartz, J., Godwin, R. T., & Giles, D. E. (2013). Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution. Journal of Statistical Computation and Simulation, 83(3), 434-445.

Examples

Run this code

se_naka(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_naka(1.2, 0.2, delta)
hce_naka(1.2, 0.2, delta)
ae_naka(1.2, 0.2, delta)

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