Interval Estimation of a P(X1 < X2) Model for Variables having General Inverse Exponential Form Distributions with Unknown Parameters
American Journal of Theoretical and Applied Statistics
Volume 7, Issue 4, July 2018, Pages: 132-138
Received: Feb. 28, 2018; Accepted: Mar. 26, 2018; Published: May 3, 2018
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Authors
N. A. Mokhlis, Department of Mathematics, Ain Shams University, Cairo, Egypt
E. J. Ibrahim, Department of Mathematics, Ain Shams University, Cairo, Egypt
D. M. Gharieb, Department of Mathematics, Ain Shams University, Cairo, Egypt
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Abstract
In this article the interval estimation of a P(X1 < X2) model is discussed when X1 and X2are non-negative independent random variables, having general inverse exponential form distributions with different unknown parameters. Different interval estimators are derived, by applying different approaches. A simulation study is performed to compare the estimators obtained. The comparison is carried out on basis of average length, average coverage, and tail errors. The results are illustrated, using inverse Weibull distribution as an example of the general inverse exponential form distribution.
Keywords
General Inverse Exponential Form Distribution, Coverage Probability, Bootstrap Confidence Interval, Generalized Pivotal Quantity
To cite this article
N. A. Mokhlis, E. J. Ibrahim, D. M. Gharieb, Interval Estimation of a P(X1 < X2) Model for Variables having General Inverse Exponential Form Distributions with Unknown Parameters, American Journal of Theoretical and Applied Statistics. Vol. 7, No. 4, 2018, pp. 132-138. doi: 10.11648/j.ajtas.20180704.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
S. Kotz, Y. Lumelskii, M. Pensky, The Stress-Strength Model and its Generalizations: Theory and Applications, Singapore: World Scientific, 2003.
[2]
D. Al-Mutairi, M. Ghitany, D. Kunddu, Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics-Theory and Methods, 8 (2013) 1443-1463.
[3]
N. Amiri, R. Azimi, F. Yaghmaei, M. Babanezhad, Estimation of stress-strength parameter for two parameter Weibull distribution, International Journal of Advanced Statistics and Probability, 1(2013) 4-8.
[4]
S. Rezaei, R. Tahmasbi, M. Mahmoodi, Estimation of P(Y < X) for generalized Pareto distribution, Statistical Planning and Inference, 140 (2010) 480-494.
[5]
N. Mokhlis, E. Ibrahim, D. Gharieb, Stress-strength reliability with general form distributions, Communications in Statistics-Theory and Methods, 46 (2017) 1230-1246.
[6]
N. Mokhlis, E. Ibrahim, D. Gharieb, Interval estimation of a P(X1 < X2) model with general form distributions for unknown parameters, Statistics Applications and Probability, 6 (2017) 391-400.
[7]
B. Efron, An Introduction to the Bootstrap, Chapman and Hall, 1994.
[8]
A. Asgharzadeh, R. Valiollahi, M. Z. Raqab, Estimation of the stress-strength reliability for the generalized logistic distribution, Statistical Methodology, 15 (2013) 73-94.
[9]
D. R. Thoman, L. J. Bain, C. E. Antle, Inferences on the parameters of the Weibull distribution, Technometrics, 11(1969) 445-446.
[10]
K. Krishnamoorthy, Y. Lin, Y. Xia, Confidence limits and prediction limits for a Weibull distribution based on the generalized variable approach, Statistical Planning and Inference, 139 (2009) 2675–2684.
[11]
K. Krishnamoorthy, Y. Lin, Confidence limits for stress-strength reliability involving Weibull models, Statistical Planning and Inference, 140 (2010) 1754-1764.
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