exp: 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 distribution

Description

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

Usage

Se_exp(alpha)
re_exp(alpha, delta)
hce_exp(alpha, delta)
ae_exp(alpha, delta)

Arguments

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

Details

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

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

where x > 0 and \alpha > 0.

Value

The functions Se_exp, re_exp, hce_exp, and ae_exp provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponential 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

Balakrishnan, K. (2019). Exponential distribution: theory, methods and applications. Routledge.

Singh, A. K. (1997). The exponential distribution-theory, methods and applications, Technometrics, 39(3), 341-341.

Arimoto, S. (1971). Information-theoretical considerations on estimation problems. Inf. Control, 19, 181–194.

See Also

re_chi, re_gamma, re_wei

Examples

Se_exp(0.2)
delta <- c(1.5, 2, 3)
re_exp(0.2, delta)
hce_exp(0.2, delta)
ae_exp(0.2, delta)

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