naka: 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 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)

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).

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.

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.

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

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.

See Also

re_exp, re_gamma, re_wei

Examples

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)

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