nh: 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 exponential extension distribution

Description

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

Usage

se_nh(alpha, beta)
re_nh(alpha, beta, delta)
hce_nh(alpha, beta, delta)
ae_nh(alpha, beta, delta)

Arguments

alpha	The strictly positive parameter of the exponential extension distribution (\alpha > 0).
beta	The strictly positive parameter of the exponential extension distribution (\beta > 0).
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

Details

The following is the probability density function of the exponential extension distribution:

f(x)=\alpha\beta(1+\alpha x)^{\beta-1}e^{1-(1+\alpha x)^{\beta}},

where x > 0, \alpha > 0 and \beta > 0.

Value

The functions se_nh, re_nh, hce_nh, and ae_nh provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponential extension 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

Nadarajah, S., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558.

See Also

re_exp, re_gamma, re_ee, re_wei

Examples

se_nh(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_nh(1.2, 0.2, delta)
hce_nh(1.2, 0.2, delta)
ae_nh(1.2, 0.2, delta)

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