shannon (version 0.2.0)

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

Description

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

Usage

rlse_wei(p, alpha, beta)
rlre_wei(p, alpha, beta, delta)
rlhce_wei(p, alpha, beta, delta)
rlae_wei(p, alpha, beta, delta)

Value

The functions rlse_wei, rlre_wei, rlhce_wei, and rlae_wei 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 Weibull distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive scale parameter of the Weibull distribution (\(\alpha > 0\)).

beta

The strictly positive shape parameter of the Weibull 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.

Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics, 18, 293-297.

See Also

re_wei

Examples

p <- c(1, 1.7, 3)
rlse_wei(p, 2, 1)
rlre_wei(p, 2, 1, 0.5)
rlhce_wei(p, 2, 1, 0.5)
rlae_wei(p, 2, 1, 0.5)