Abstract
We consider the problem of minimum risk point estimation for the parameter θ=aμ+bσ of the exponential distribution with unknown location parameter μ and scale parameter σ when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of θ and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chow, Y. S., Hsiung, C. A. and Lai, T. L. (1979). Extended renewal theory and moment convergence in Anscombe's theorem,Ann. Probab.,7, 304–318.
Ghosh, M. and Mukhopadhyay, N. (1989). Sequential estimation of the percentiles of exponential and normal distributions,South African Statist. J.,23, 251–268.
Lombard, F. and Swanepoel, J. W. H. (1978). On finite and infinite confidence sequences,South African Statist. J.,12, 1–24.
Mukhopadhyay, N. (1987). Minimum risk point estimation of the mean of a negative exponential distribution,Sankhyā Ser. A,49, 105–112.
Mukhopadhyay, N. and Ekwo, M. E. (1987). A note on minimum risk point estimation of the shape parameter of a Pareto distribution,Calcutta Statist. Assoc. Bull.,36, 69–78.
Woodroofe, M. (1977). Second order approximations for sequential point and interval estimation,Ann. Statist.,5, 984–995.
Woodroofe, M. (1982).Nonlinear Renewal Theory in Sequential Analysis, CBMS Monograph No. 39, SIAM, Philadelphia.
Author information
Authors and Affiliations
About this article
Cite this article
Isogal, E., Uno, C. Sequential estimation of a parameter of an exponential distribution. Ann Inst Stat Math 46, 77–82 (1994). https://doi.org/10.1007/BF00773594
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773594