On the Effect of Decimal Corrections on Errors of Observation
Hartman, Philip ; Wintner, Aurel
Ann. Math. Statist., Tome 19 (1948) no. 4, p. 389-393 / Harvested from Project Euclid
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 $\sigma$.
Publié le : 1948-09-14
Classification: 
@article{1177730203,
     author = {Hartman, Philip and Wintner, Aurel},
     title = {On the Effect of Decimal Corrections on Errors of Observation},
     journal = {Ann. Math. Statist.},
     volume = {19},
     number = {4},
     year = {1948},
     pages = { 389-393},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177730203}
}
Hartman, Philip; Wintner, Aurel. On the Effect of Decimal Corrections on Errors of Observation. Ann. Math. Statist., Tome 19 (1948) no. 4, pp.  389-393. http://gdmltest.u-ga.fr/item/1177730203/