Abstract
In selection processes of a random variable with random observation errors, the crucial variable is the conditional expectation of the target variable given the sum of the observations. An example is the selection of the most talented young researchers for tenure track. This paper derives an explicit expression for this conditional expectation for the case that both the target variable and the observation errors have a uniform, but different, distribution.
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Sadooghi-Alvandi SM, Nematollahi AR, Habibi R (2009) On the distribution of the sum of independent uniform random variables. Stat Pap 50: 171–175
Acknowledgements
I would like to thank Ludo Waltman of CWTS and an anonymous referee for comments that improved the presentation.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Van Bochove, C.A. Expectation of a uniform random variable with uniform observation errors after selection of the highest observations. Stat Papers 52, 971–977 (2011). https://doi.org/10.1007/s00362-009-0304-y
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DOI: https://doi.org/10.1007/s00362-009-0304-y