Estimation of P {X <= Y } for geometric-Poisson model
Estimation of P {X <= Y } for geometric-Poisson model
In this paper we estimate R = P {X
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- Ahmad, K. E., Fakhry, M. E. and Jaheen Z. F. Bayes estimation of P (Y > X) in the geometric case, Microelectronic Reliability 35(5), 817-820, 1995.
- Baklizi, A. and Quader El-Masri, A. E. Shrinkage estimation of P (X _____ Y ) in the exponential case with common location parameter, Metrika 59, 163-171, 2004.
- Belyaev, Y. and Lumelskii, Y. Multidimensional Poisson Walks, Journal of Mathematical Sciences 40, 162-165, 1988.
- Birnbaum, Z. W. On a Use of Mann-Whitney Statistics, Proc. Third Berkeley Symp. in Math. Statist. Probab. 1 (University of California Press, Berkeley, 1956), 13-17.
- Constantine, K. and Carson, M. The estimation of P (Y _____ X) in the gamma case, Commu- nications in Statistics: Simulation and Computation 15, 365-388, 1986.
- Constantine, K., Carson, M. and Tse, S.K. Confidence Interval Estimation of P (Y _____ X) in the Gamma Case, Communications in Statistics: Simulation and Computation 19(1), 225-244, 1990. [7] Downtown, F. On the Estimation of P r(Y _____ X) in the Normal Case, Technometrics 15, 551-558, 1973. [8] Genç, A. I. Estimation of P (X > Y ) with Topp-Leone Distribution, Journal of Statistical Computation and Simulation 83(2), 326-339, 2013.
- Govidarajulu, Z. Two sided confidence limits for P (X > Y ) based on normal samples of X and Y , Sankhyã 29, 35-40, 1967.
- Hall, P. Theoretical comparison of bootstrap confidence intervals, Annals of Statistics 16, 927-953, 1988. [11] Hogg, R. V., McKean, J. W. and Craig, A. T. Introduction to Mathematical Statistics, Sixth Edition (Pearson Prentice Hall, New Jersey, 2005), 348-349.
- Ismail, R., Jeyaratnam, S. S. and Panchapakesan, S. Estimation of P r[X > Y ] for Gamma Distributions, Journal of Statistical Computation and Simulation 26(3-4), 253-267, 1986.
- Ivshin, V. V. and Lumelskii, Ya. P. Statistical Estimation Problems in "Stress-Strength" Models (Perm University Press, Perm, Russia, 1995).
- Kakade, C. S., Shirke, D. T. and Kundu, D. Inference for P (Y _____ X) in exponentiated Gumbel distribution, Journal of Statistics and Applications 3(1-2), 121-133, 2008.
- Kotz, S., Lumelskii, Y. and Pensky, M. The Stress-Strength Model and its Generalizations (World Scientific Press, Singapore, 2003).
- Kundu, D. and Gupta, R. D. Estimation of P [Y _____ X] for Generalized Exponential Distri- bution, Metrika 61, 291-308, 2005.
- Kundu, D. and Gupta, R. D. Estimation of P [Y _____ X] for Weibull Distributions, IEEE Transactions on Reliability 55(2), 270-280, 2006.
- Lumelskii, Ya. P. Unbiased sufficient estimators of probabilities in the case of multivariate normal distribution, Vest. MGU, Mathematics 6 (in Russian), 14-17, 1968.
- Maiti, S. S. Estimation of P (X _____= Y ) in the geometric case, Journal of Indian Statistical Association 33, 87-91, 1995.
- Owen, D. B., Craswell, K. J. and Handson, D. L. Non-parametric upper confidence bounds for P (Y _____ X) and confidence limits for P (Y _____ X) when X and Y are normal, Journal of American Statistical Association 59, 906-924, 1964.
- Rezaei, S., Tahmasbi, R. and Mahmoodi, M. Estimation of P [Y _____ X] for Generalized Pareto Distribution, Journal of Statistical Planning and Inference 140, 480-494, 2010.
- Saraçoglu, B., Kaya, M. F. and Abd-Elfattah, A. M. Comparison of Estimators for Stress- Strength Reliability in the Gompertz Case, Hacettepe Journal of Mathematics and Statistics 38(3), 339-349, 2009.
- Sathe, Y. S. and Dixit, U. J. Estimation of P (X _____= Y ) in the negative binomial distribution, Journal of Statistical Planning and Inference 93, 83-92, 2001.
- Tong, H. A Note on the Estimation of P (Y _____ X) in the Exponential Case, Technometrics 16, 625. Errata: Technometrics 17, 395, 1974.
- Tong, H. On the Estimation of P (Y _____ X) for Exponential Families, IEEE Transactions in Reliability 26, 54-56, 1977.
- Woodward, W. A. and Kelley, G. D. Minimum variance unbiased estimation of P (X _____ Y ) in the normal case, Technometrics 19, 95-98, 1977.