shannon (version 0.2.0)

Truncated exponential extension distribution: Relative loss for various entropy measures using the truncated exponential extension distribution

Description

Compute the relative information loss of the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the truncated exponential extension distribution.

Usage

rlse_nh(p, alpha, beta)
rlre_nh(p, alpha, beta, delta)
rlhce_nh(p, alpha, beta, delta)
rlae_nh(p, alpha, beta, delta)

Value

The functions rlse_nh, rlre_nh, rlhce_nh, and rlae_nh provide the relative information loss based on the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the truncated exponential extension distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive parameter of the exponential extension distribution (\(\alpha > 0\)).

beta

The strictly positive parameter of the exponential extension distribution (\(\beta > 0\)).

p

The truncation time \((p>0)\).

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 .

References

Awad, A. M., & Alawneh, A. J. (1987). Application of entropy to a life-time model. IMA Journal of Mathematical Control and Information, 4(2), 143-148.

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

See Also

re_nh

Examples

p <- c(0.25, 0.50, 0.75)
rlse_nh(p, 1.2, 0.2)
rlre_nh(p, 1.2, 0.2, 0.5)
rlhce_nh(p, 1.2, 0.2, 0.5)
rlae_nh(p, 1.2, 0.2, 0.5)