Abstract
Fisher’s amount of information I for a location family of distributions with variance 1 attains its minimum value 1 if and only if the family is normal. This characterization of normality is stable in the sense that the distribution is nearly normal whenever I is close to 1. The stability is, together with some other characteristic properties of the normal distribution, used to prove the central limit theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kagan, A. M., Linnik, Yu. V., and Rao, C. R. (1973). Characterization Problems in Mathematical Statistics. John Wiley, New York.
Kudo, H. (1957). Mathematical Statistics. Kyoritsu Pub., Tokyo. (In Japanese).
Kullback, S. (1968). Information and Statistics. Dover.
Linnik, Yu. V. (1959). Theor. Probab. Appl. 4, 288–299.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Shimizu, R. (1975). On Fisher’s Amount of Information for Location Family. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1848-7_28
Download citation
DOI: https://doi.org/10.1007/978-94-010-1848-7_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1850-0
Online ISBN: 978-94-010-1848-7
eBook Packages: Springer Book Archive