Open Access
September, 1948 On the Effect of Decimal Corrections on Errors of Observation
Philip Hartman, Aurel Wintner
Ann. Math. Statist. 19(3): 389-393 (September, 1948). DOI: 10.1214/aoms/1177730203


Let $t$ be the true value of what is being measured and suppose that the error of observation is a symmetric normal distribution of standard deviation $\sigma$. The "rounding-off" error due to the reading of measurements to the nearest unit has a distribution and an expected value depending on $t$ and $\sigma$. It is shown that, for a fixed $\sigma > 0$, the expected value of the decimal correction, $r(t; \sigma)$, is an analytic function of $t$ which is odd, of period 1, positive for $0 < t < \frac{1}{2}$, and has a convex arch as its graph on $0 \leqq t \leqq \frac{1}{2}$. Furthermore, if $0 < t < \frac{1}{2}$, both $r(t; \sigma)$ and its maximum value, $\operatorname{Max}_t r(t; \sigma)$, are decreasing functions of $\sigma$.


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Philip Hartman. Aurel Wintner. "On the Effect of Decimal Corrections on Errors of Observation." Ann. Math. Statist. 19 (3) 389 - 393, September, 1948.


Published: September, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0037.37006
MathSciNet: MR26442
Digital Object Identifier: 10.1214/aoms/1177730203

Rights: Copyright © 1948 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1948
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