shannon (version 0.2.0)

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

Description

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

Usage

rlse_kum(p, alpha, beta)
rlre_kum(p, alpha, beta, delta)
rlhce_kum(p, alpha, beta, delta)
rlae_kum(p, alpha, beta, delta)

Value

The functions rlse_kum, rlre_kum, rlhce_kum, and rlae_kum 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 Kumaraswamy distribution, \(p\) and \(\delta\).

Arguments

alpha

The strictly positive shape parameter of the Kumaraswamy distribution (\(\alpha > 0\)).

beta

The strictly positive shape parameter of the Kumaraswamy 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.

El-Sherpieny, E. S. A., & Ahmed, M. A. (2014). On the Kumaraswamy distribution. International Journal of Basic and Applied Sciences, 3(4), 372.

Al-Babtain, A. A., Elbatal, I., Chesneau, C., & Elgarhy, M. (2021). Estimation of different types of entropies for the Kumaraswamy distribution. PLoS One, 16(3), e0249027.

See Also

re_kum

Examples

p <- c(0.25, 0.50, 0.75)
rlse_kum(p, 0.2, 0.4)
rlre_kum(p, 0.2, 0.4, 0.5)
rlhce_kum(p, 0.2, 0.4, 0.5)
rlae_kum(p, 0.2, 0.4, 0.5)