Volume 26 , Issue 4 , PP: 137-142, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Naser Odat 1 *
Doi: https://doi.org/10.54216/IJNS.260413
This work focuses on the estimation reliability function where x and y are two independent Benktander distributions. The greatest likelihood's asymptotic distribution is found. The maximum likelihood estimator, the moment method estimator, and the approximate maximum likelihood estimator of are proposed. We obtain the asymptotic distribution of s maximum likelihood estimate. The confidence interval can be found using the asymptotic distribution.
Benktander , Maximum likelihood , Asymptotic distribution , Fisher information matrix
[1] K. Constantine and M. Karson, "The Estimation of P(Y<X) in Gamma Case," Commun. Stat. Simul. Compute, vol. 15, pp. 365-388, 1986.
[2] K. Constantine, M. Karson, and S. K. Tse, "Confidence Interval Estimation of P(Y<X) in the Gamma Case," Commun. Stat. Simul. Compute, vol. 19, no. 1, pp. 225-244, 1990.
[3] F. Downtown, "The Estimation of P(Y<X) in the Normal Case," Technometrics, vol. 15, pp. 551-558, 1973.
[4] Tong, "On the estimation for the exponential families," IEEE Trans. Reliab., vol. 26, pp. 54-56, 1977.
[5] R. Ismail, S. S. Jeyaratnam, and S. Panchapakesan, "Estimation of Pr[X>Y] for Gamma Distributions," J. Stat. Comput. Simul, vol. 26, no. 3-4, pp. 253-267, 1986.
[6] S. Nadarajah, "Reliability for Logistic Distributions," Elektron. Model, vol. 26, no. 3, pp. 65-82, 2004.
[7] R. Hatamleh and V. A. Zolotarev, "On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component," J. Math. Phys. Anal. Geom., vol. 11, no. 2, pp. 174–186, 2015, doi: 10.15407/mag11.02.174.
[8] J. I. McCool, "Inference on P(Y < X) in the Weibull Case," Commun. Stat. Simul. Compute, vol. 20, pp. 129-148, 1991.
[9] A. M. Awad, M. M. Azzam, and M. A. Hamadan, "Some inference results in P(Y < X) in the bivariate exponential model," Commun. Stat. Theory Methods, vol. 10, pp. 2515-2524, 1981.
[10] J. D. Church and B. Harris, "The estimation of reliability from stress-strength relationships," Technometrics, vol. 12, pp. 49-54, 1970.
[11] F. Downtown, "The estimation of P(X > Y) in the normal case," Technometrics, vol. 15, pp. 551-558, 1973.
[12] Z. Govidarajulu, "Two-sided confidence limits for P(X > Y) based on normal samples of X and Y," Sankhya B, vol. 29, pp. 35-40, 1967.
[13] A. Hazaymeh, "Time-Shadow Soft Set: Concepts and Applications," Int. J. Fuzzy Logic Intell. Syst., vol. 24, no. 4, pp. 387-398, 2024.
[14] A. Hazaymeh and A. Bataihah, "Results on Fixed Points in Neutrosophic Metric Spaces Through the Use of Simulation Functions," J. Math. Anal., vol. 15, no. 6, pp. 47–57, 2024.
[15] J. K. Lee, "A Study on the Impact of AI on Business Processes," IEEE Access, vol. 9, pp. 12345-12356, 2021.
[16] M. R. Alshahrani, "Machine Learning Techniques for Predicting Customer Behavior," Future Gener. Comput. Syst., vol. 115, pp. 567-578, 2021.
[17] P. Patel, "Data Analytics for Enhanced Decision Making in Supply Chains," Comput. Ind. Eng., vol. 160, pp. 107-115, 2021.
