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Estimation of $$P(X>Y)$$ with Topp-Leone distribution. (English) Zbl 1348.62039
Summary: We consider the estimation problem of the probability $$P=P(X>Y)$$ for the standard Topp-Leone distribution. After discussing the maximum likelihood and uniformly minimum variance unbiased estimation procedures for the problem on both complete and left censored samples, we perform a Monte Carlo simulation to compare the estimators based on the mean square error criteria. We also consider the interval estimation of $$P$$.

##### MSC:
 62E15 Exact distribution theory in statistics 60E05 Probability distributions: general theory 62F10 Point estimation 62N01 Censored data models
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##### References:
 [1] DOI: 10.2307/1267617 · Zbl 0292.62021 [2] DOI: 10.1007/BF01893574 · Zbl 0436.62029 [3] DOI: 10.1007/BF02362481 · Zbl 0863.62017 [4] DOI: 10.1007/s00362-006-0034-3 · Zbl 1312.62129 [5] DOI: 10.1007/s001840400345 · Zbl 1079.62032 [6] DOI: 10.1109/24.406571 · Zbl 04527632 [7] DOI: 10.1080/03610918608812514 · Zbl 0606.62110 [8] DOI: 10.1081/STA-200063183 · Zbl 1070.62091 [9] DOI: 10.1080/00949658608810967 · Zbl 0609.62129 [10] Nadarajah S., Serdica Math. J 28 pp 267– (2002) [11] DOI: 10.1142/9789812564511 [12] Barlow R. E., Statistical Theory of Reliability and Life Testing: Probability Models (1975) · Zbl 0379.62080 [13] DOI: 10.1080/01621459.1955.10501259 [14] Nadarajah S., J. Appl. Statist 30 pp 311– (2003) · Zbl 1121.62448 [15] DOI: 10.1142/9789812701282 [16] DOI: 10.1080/02664760500079613 · Zbl 1121.62374 [17] Kotz S., Encylopedia of Statistical Sciences 6 pp 3786–, 2. ed. (2006) [18] Ghitany M. E., Int. J. Appl. Math 20 pp 371– (2007) [19] Genç A. \.I., Stat. Pap [20] DOI: 10.1080/02664760802230583 · Zbl 1273.62041 [21] Gradshteyn I. S., Table of Integrals, Series, and Products, 6. ed. (2000) · Zbl 0981.65001 [22] Birnbaum , Z. W.On a use of the Mann–Whitney Statistic. Proceedings of the Third Berkeley Symposium on Mathematical. Statistics and Probability . Edited by: Neyman , J. Vol. 1 , pp. 13 – 17 . Berkeley , CA : University of California Press . · Zbl 0071.35504 [23] Bain L. J., Statistical Analysis of Reliability and Life-Testing Models, 2. ed. (1991) · Zbl 0724.62096 [24] DOI: 10.1214/aoms/1177728793 · Zbl 0056.38203 [25] DOI: 10.1016/0142-0615(83)90011-X [26] DOI: 10.1080/00401706.1984.10487942
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