期刊
STATISTICS & PROBABILITY LETTERS
卷 81, 期 8, 页码 1179-1182出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spl.2011.03.014
关键词
Cumulative distribution function (CDF); Folded CDF; Mean absolute deviation (MAD) from the median
资金
- EU-PASCAL2 Network of Excellence
The aims of this short note are two-fold. First, it shows that, for a random variable X, the area under the curve of its folded cumulative distribution function equals the mean absolute deviation (MAD) from the median. Such an equivalence implies that the MAD is the area between the cumulative distribution function (CDF) of X and that for a degenerate distribution which takes the median as the only value. Secondly, it generalises the folded CDF to a p-folded CDF, and derives the equivalence between the area under the curve of the p-folded CDF and the weighted mean absolute deviation from the p-quantile (MAD(p)). In addition, such equivalences give the MAD and MAD(p) simple graphical interpretations. Some other practical implications are also briefly discussed. (C) 2011 Elsevier B.V. All rights reserved.
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