Mean Streets: The Median of a Size-Biased Sample and the Population Mean
作者:
Woollcott Smith,
Milton Parnes,
期刊:
The American Statistician
(Taylor Available online 1994)
卷期:
Volume 48,
issue 2
页码: 106-110
ISSN:0003-1305
年代: 1994
DOI:10.1080/00031305.1994.10476034
出版商: Taylor & Francis Group
关键词: Point processes;Sampled Poisson process;Weighted distributions
数据来源: Taylor
摘要:
In a size-biased or weighted sample, the probability that a unit is sampled depends on a property of the sampling unit. Cars sampled by an observer traveling at a fixed velocity, v0, can be modeled as a size-biased sample because a car with a large absolute difference between its velocity and v0, is more likely to be sampled. A consistent estimator of the population mean velocity is found that depends solely on counts of the number of cars the observer passes and the number of cars that pass the observer. This estimator has the unusual property that when counts of passed and passing cars are equal, the sample median velocity and the estimated population mean velocity are both the observer's velocity, v0.
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