Quantile

A Quantile is a member of a quantile distribution.

• Example(s):
  • Tercile.
  • Quartile.
  • Quintile.
  • Decile.
  • Percentile.
• See: Quantile Function, Cumulative Distribution Function, Random Variable.

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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]\displaystyle{ q }[/math] essentially equal-sized data subsets is the motivation for [math]\displaystyle{ q }[/math]-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets. Put another way, a [math]\displaystyle{ k^\mathrm{th} }[/math] [math]\displaystyle{ q }[/math]-quantile for a random variable is a value [math]\displaystyle{ x }[/math] such that the probability that the random variable will be less than [math]\displaystyle{ x }[/math] is at most [math]\displaystyle{ k/q }[/math] and the probability that the random variable will be greater than [math]\displaystyle{ x }[/math] is at most [math]\displaystyle{ (q-k)/q=1-(k/q) }[/math]. There are [math]\displaystyle{ q-1 }[/math] of the [math]\displaystyle{ q }[/math]-quantiles, one for each integer [math]\displaystyle{ k }[/math] satisfying [math]\displaystyle{ 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.

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/quantile#Specialized_quantiles Retrieved:2015-1-29.
  • Some q-quantiles have special names:*The 2-quantile is called the median.
    • The 3-quantiles are called tertiles or terciles → T
    • The 4-quantiles are called quartiles → Q
    • The 5-quantiles are called quintiles → QU
    • The 6-quantiles are called sextiles → S
    • The 10-quantiles are called deciles → D
    • The 12-quantiles are called duo-deciles → Dd
    • The 20-quantiles are called vigintiles → V
    • The 100-quantiles are called percentiles → P
    • The 1000-quantiles are called permilles → Pr
  • More generally, one can consider the quantile function for any distribution. This is defined for real variables between zero and one and is mathematically the inverse of the cumulative distribution function.

2009

• http://en.wiktionary.org/wiki/quantile#Noun
  • (statistics) One of the class of values of a variate which divides the members of and batch or sample into equal-sized subgroups of adjacent values or a probability distribution into distributions of equal probability.

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