Abstract
Both one-sample and multi-sample estimation problems for the means of one parameter exponential distributions are addressed. In the one-sample case, for the existing purely sequential and recently obtained piecewise sequential estimation methodologies, we follow and extend the development in Isogai and Uno (1993,Ann. Inst. Statist. Math. (in press)) in order to obtain a class of estimators that provides asymptotic second-order risk improvement. In the multi-sample problem, we address the analogous aspects for the existing purely sequential methodology as well as the newly developed piecewise methodology.
Similar content being viewed by others
References
Bose, A. and Mukhopadhyay, N. (1993). Sequential estimation of the mean of an exponential distribution via replicated piecewise stopping number, Tech. Report, No. 93-06, Department of Statist., University of Connecticut, Storrs.
Ghosh, M. and Mukhopadhyay, N. (1989). Sequential estimation of the percentiles of exponential and normal distributions,South African Statist. J.,23, 251–268.
Isogai, E. and Uno, C. (1992). On the sequential point estimation of the mean of a gamma distribution (submitted).
Isogai, E. and Uno, C. (1993). Sequential estimation of a parameter of an exponential distribution,Ann. Inst. Statist. Math. (in press).
Mukhopadhyay, N. (1987). Minimum risk point estimation of the mean of a negative exponential distribution,Sankhyā Ser. A,49, 105–112.
Mukhopadhyay, N. and Chattopadhyay, S. (1991). Sequential methodologies for comparing exponential mean survival times,Sequential Anal.,10, 139–148.
Mukhopadhyay, N. and Sen, P. K. (1993). Replicated piecewise stopping numbers and sequential analysis,Sequential Anal.,12, 179–197.
Starr, N. and Woodroofe, M. (1972). Further remarks on sequential estimation: The exponential case,Ann. Math. Statist.,43, 1147–1154.
Woodroofe, M. (1977). Second order approximations for sequential point and interval estimation,Ann. Statist.,5, 985–995.
Author information
Authors and Affiliations
About this article
Cite this article
Mukhopadhyay, N. Improved sequential estimation of means of exponential distributions. Ann Inst Stat Math 46, 509–519 (1994). https://doi.org/10.1007/BF00773514
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773514