shannon (version 0.2.0)

Chi-squared distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Chi-squared distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the chi-squared distribution.

Usage

se_chi(n)
re_chi(n, delta)
hce_chi(n, delta)
ae_chi(n, delta)

Value

The functions se_chi, re_chi, hce_chi, and ae_chi provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Chi-squared distribution and \(\delta\).

Arguments

n

The degree of freedom and the positive parameter of the Chi-squared distribution (\(n > 0\)).

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 .

Details

The following is the probability density function of the (non-central) Chi-squared distribution: $$ f(x)=\frac{1}{2^{\frac{n}{2}}\Gamma(\frac{n}{2})}x^{\frac{n}{2}-1}e^{-\frac{x}{2}}, $$ where \(x > 0\) and \(n > 0\), and \(\Gamma(a)\) denotes the standard gamma function.

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.

See Also

re_exp, re_gamma, re_bs

Examples

se_chi(1.2)
delta <- c(0.2, 0.3)
re_chi(1.2, delta)
hce_chi(1.2, delta)
ae_chi(1.2, delta)