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

Description

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

Usage

se_norm(alpha, beta)
re_norm(alpha, beta, delta)
hce_norm(alpha, beta, delta)
ae_norm(alpha, beta, delta)

Value

The functions se_norm, re_norm, hce_norm, and ae_norm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Normal distribution and $\delta$.

Arguments

alpha: The location parameter of the normal distribution ($\alpha\in\left(-\infty,+\infty\right)$).
beta: The strictly positive scale parameter of the normal 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 normal distribution: $$ f(x)=\frac{1}{\beta\sqrt{2\pi}}e^{-0.5\left(\frac{x-\alpha}{\beta}\right)^{2}}, $$ where $x\in\left(-\infty,+\infty\right)$, $\alpha\in\left(-\infty,+\infty\right)$ and $\beta > 0$. The parameters $\alpha$ and $\beta$ represent the mean and standard deviation, respectively.

References

Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.

Examples

Run this code

se_norm(0.2, 1.4)
delta <- c(1.5, 2, 3)
re_norm(0.2, 1.4, delta)
hce_norm(0.2, 1.4, delta)
ae_norm(0.2, 1.4, delta)

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