Derivation of Cumulative Residual Entropy for a Modified Skewed Distribution
Main Article Content
Abstract
In this paper, the derivation of cumulative residual entropy which makes use of a probability distribution survival function for the derivation is presented. The entropy is derived for of a distribution introduced by Nkombou et al. (2025) called DUS Skew Student-t (DUSSS-t) Distribution. Specifically, the entropy derived is the Cumulative Residual Renyi Entropy (CRRE). The final result shows it is possible that other cumulative residual entropy for the DUSSS-t can be estimated following the same approach in this paper.
Downloads
Article Details

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
AI-Babtain, A. A, Hassan, A. S, Zaky. A. N, Elbatal, I. & Elgarhy, M. (2021). Dynamic cumulative residual Renyi entropy for Lomax distribution: Bayesian and non-Bayesian methods. AIMS Mathematics, 6(4), 3889-3914, https:// doi.10.3934/math.2021231.
David, I. J., Mathew, S., & Falgore, J. Y. (2024). New Sine Inverted Exponential Distribution: Properties, Simulation and Application. European Journal of Statistics, 4(5), https://doi.10.28924/ada/stat.4.5.
David, I. J., Okeke, E. N., & Franklin, L. (2024). A Modified Ailamujia Diatribution: Properties and Application. Reliability Theory & Application, 19(3), 638-652.
Eghwerido, J. T., David, I. J., & Adubisi, O. D. (2020). Inverse Odd Weibul Generated Family of Distributions. Pakistan Journal of Statistics and Operations Research, 16(3), 617-633.
Hartley, R. V. L. (1928) Transmission of information. Bell Systems Technical Journal, 7(3), 535-563.
Mathew, S. David, I. J., & Yaska, M. (2024). A Study on One-Parameter Entropy-Transformed Exponential Distribution and Its Application. Journal of Reliability and Statistical Studies, 17(1), 17-44.
Nkombou, M. B. W. (2025). Heteroscedastic regression modelling using DUS Transformed Skewed Error Innovation Distributions. Unpublished Ph.D. Thesis, Federal University Wukari, Nigeria.
Nyquist, H. (1924). Certain Factors Affecting Telegraph Speed. Bell Systems Technical Journal, 3(2), 324-346.
Nyquist, H. (1928). Certain Topics in Telegraph Transmission Theory. Transactions of the American Institute of Electrical Engineers, 47, 617-644.
Rao, M., Chen, Y. & Vemuri, B. (2004). Cumulative residual entropy: a new measure of information. IEEE Transactions on Information Theory 50(6), 1220-1228.
Rényi, A. (1961). On Measures of Entropy and Information, in `Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics', Vol. 4, University of California Press, pp. 547-562.
Shannon, C. E. (1948). A mathematical theory of communication. Bell Systems Technical Journal, 27, 379–423.
Taboga, M. (2017). Lectures on Probability Theory and Mathematical Statistics. 3rd ed. John Wiley & Sons, New York.
Zardasht, V. (2022). On Cumulative Residual Renyi's Entropy. Revista Colombiana de Estadística- Theorical Statistics. 45(2), 257-273.




















