shannon (version 0.2.0)

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

Description

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

Usage

rlse_gum(p, alpha, beta)
rlre_gum(p, alpha, beta, delta)
rlhce_gum(p, alpha, beta, delta)
rlae_gum(p, alpha, beta, delta)

Value

The functions rlse_gum, rlre_gum, rlhce_gum, and rlae_gum 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 Gumbel distribution, \(p\) and \(\delta\).

Arguments

alpha

The location parameter of the Gumbel distribution (\(\alpha\in\left(-\infty,+\infty\right)\)).

beta

The strictly positive scale parameter of the Gumbel 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.

Gomez, Y. M., Bolfarine, H., & Gomez, H. W. (2019). Gumbel distribution with heavy tails and applications to environmental data. Mathematics and Computers in Simulation, 157, 115-129.

See Also

re_gum

Examples

p <- c(1.8,2.2)
rlse_gum(p, 4, 2)
rlre_gum(p, 4, 2, 2)
rlhce_gum(p, 4, 2, 2)
rlae_gum(p, 4, 2, 2)