Quantile

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A Quantile is a member of a quantile distribution.



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/quantile Retrieved:2015-1-29.
    • Quantiles are values taken at regular intervals from the inverse of the cumulative distribution function (CDF) of a random variable. Dividing ordered data into [math]q[/math] essentially equal-sized data subsets is the motivation for [math]q[/math]-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets. Put another way, a [math]k^\mathrm{th}[/math] [math]q[/math]-quantile for a random variable is a value [math]x[/math] such that the probability that the random variable will be less than [math]x[/math] is at most [math]k/q[/math] and the probability that the random variable will be greater than [math]x[/math] is at most [math](q-k)/q=1-(k/q)[/math]. There are [math]q-1[/math] of the [math]q[/math]-quantiles, one for each integer [math]k[/math] satisfying [math]0 \lt k \lt q[/math]. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median of a uniform probability distribution on a set of even size.


2009