Abstract
A loss function proposed by Wasan (1970) is well-fitted for a measure of inaccuracy for an estimator of a scale parameter of a distribution defined onR +=(0, ∞). We refer to this loss function as the K-loss function. A relationship between the K-loss and squared error loss functions is discussed. And an optimal estimator for a scale parameter with known coefficient of variation under the K-loss function is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnholt, A. T. and Hebert, J. L. (1995). Estimating the mean with known coefficient of variation,American Statistician,49, 367–369.
Gleser, L. J. and Healy, J. D. (1976). Estimating the mean of a normal distribution with known coefficient of variation,Journal of the American Statistical Association,71, 977–981.
Hirano, K. and Iwase, K. (1989). Minimum risk equivariant estimator: Estimating the mean of an inverse Gaussian distribution with known coefficient of variation,Communications in Statistics-Theory and Methods,18, 189–197.
Iwase, K. (1989). Linear regression through the origin with constant coefficient of variation for the inverse Gaussian distribution,Communications in Statistics-Theory and Methods,18, 3587–3593.
Iwase, K. (1995). A consideration with the SN ratio for the Taguchi method,Technical Report No. 95-D1, Department of Applied Mathematics, Hiroshima University, Japan. (in Japanese)
Iwase, K. and Hirano, K. (1990). Power inverse Gaussian distribution and its applications,Japanese Journal of Applied Statistics,19, 163–176 (in Japanese)
Iwase, K. and Seto, N. (1990). Some statistical characteristics of the relation between atmospheric aluminium and scandium concentration,Bulletin of the Faculty of Engineering, Hiroshima University, Japan,38, 153–161. (in Japanese)
Khan, R. A. (1968). A note on estimating the mean of a normal distribution with known coefficient of variation,Journal of the American Statistical Association,63, 1039–1041.
Searls, D. T. (1964). The utilization of known coefficient of variation in the estimation procedure,Journal of the American Statistical Association,59, 1225–1226.
Shuster, J. (1968). On the inverse Gaussian distribution function,Journal of the American Statistical Association,63, 1514–1516.
Wasan, M. T. (1970).Parametric Estimation. McGraw-Hill Book Company, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kanefuji, K., Iwase, K. Estimation for a scale parameter with known coefficient of variation. Statistical Papers 39, 377–388 (1998). https://doi.org/10.1007/BF02927100
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02927100