Abstract
Let random samples of equal sizes be drawn from two exponential distributions with ordered means λ i . The maximum likelihood estimator λ i * of λ i is shown to have a smaller mean square error than that of the usual estimator Xi, for each i=1,2. The asymptotic efficiency of λ i * relative to Xi has also been found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions, Wiley, New York.
Blumenthal, S. and Cohen, A. (1968). Estimation of two ordered translation parameters, Ann. Math. Statist., 39, 517–530.
Cohen, A. and Sackrowitz, H. B. (1970). Estimation of last mean of monotone sequence, Ann. Math. Statist., 41, 2021–2034.
Doksum, K. and Yandell, B. S. (1984). Tests for exponentiality, Handbook of Statistics, Vol. 4, (eds. P. R. Krishnaiah and P. K. Sen), p. 579, North-Holland, Amsterdam.
Feller, W. (1957). An Introduction to Probability Theory and Its Applications, Vol. I, Second ed., Wiley, New York.
Feltz, C. J. and Dykstra, R. L. (1985). Maximum likelihood estimation of the survival functions of N stochastically ordered random variables, J. Amer. Statist. Assoc., 80, 1012–1019.
Hollander, M. and Proschan, F. (1984). Nonparametric concepts and methods in reliability, Handbook of Statistics, Vol. 4, (eds. P. R. Krishnaiah and P. K. Sen), p. 613, North-Holland, Amsterdam.
Kushary, D. and Cohen, A. (1989). Estimation of ordered Poisson parameters, Preprint, Rutgers University, New Brunswick, New Jersey.
Lee, C. I. C. (1981). The quadratic loss of isotonic regression under normality, Ann. Statist., 9, 686–688.
Marshal, A. W. and Proschan, F. (1965). Maximum likelihood estimation for distributions with monotone failure rate, Ann. Math. Statist., 36, 69–77.
Meyer, P. L. (1970). Introductory Probability and Statistical Applications, 2nd ed., Oxford and IBH Publishing, New Delhi.
Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference, Wiley, New York.
Sackrowitz, H. B. (1970). Estimation of monotone parameter sequences. The discrete case, Ann. Math. Statist., 41, 609–620.
Author information
Authors and Affiliations
About this article
Cite this article
Kaur, A., Singh, H. On the estimation of ordered means of two exponential populations. Ann Inst Stat Math 43, 347–356 (1991). https://doi.org/10.1007/BF00118640
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00118640