kumnorm: 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 Kumaraswamy normal distribution

Description

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

Usage

se_kumnorm(mu, sigma, a, b)
re_kumnorm(mu, sigma, a, b, delta)
hce_kumnorm(mu, sigma, a, b, delta)
ae_kumnorm(mu, sigma, a, b, delta)

Arguments

mu	The location parameter of the normal distribution (\mu\in\left(-\infty,+\infty\right)).
sigma	The strictly positive scale parameter of the normal distribution (\sigma > 0).
a	The strictly positive shape parameter of the Kumaraswamy distribution (a > 0).
b	The strictly positive shape parameter of the Kumaraswamy distribution (b > 0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Details

The following is the probability density function of the Kumaraswamy normal distribution:

f(x)=\frac{ab}{\sigma}\phi\left(\frac{x-\mu}{\sigma}\right)\left[\Phi\left(\frac{x-\mu}{\sigma}\right)\right]^{a-1}\left[1-\Phi\left(\frac{x-\mu}{\sigma}\right)^{a}\right]^{b-1},

where x\in\left(-\infty,+\infty\right), \mu\in\left(-\infty,+\infty\right), \sigma > 0, a > 0 and b > 0, and the functions \phi(t) and \Phi(t) , denote the probability density function and cumulative distribution function of the standard normal distribution, respectively.

Value

The functions se_kumnorm, re_kumnorm, hce_kumnorm, and ae_kumnorm provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Kumaraswamy normal 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

Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.

See Also

re_norm, re_kum

Examples

se_kumnorm(0.2, 1.5, 1, 1)
delta <- c(1.5, 2, 3)
re_kumnorm(1.2, 1, 2, 1.5, delta)
hce_kumnorm(1.2, 1, 2, 1.5, delta)
ae_kumnorm(1.2, 1, 2, 1.5, delta)

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