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quantiles

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Definitions of quantiles in various dictionaries:

noun - any of the values of a random variable that divides a frequency distribution

QUANTILES - In statistics and probability quantiles are cut points dividing the range of a probability distribution into contiguous intervals with equal probabil...

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Plural form of quantile.
Each of any set of values of a variate which divide a frequency distribution into equal groups, each containing the same fraction of the total population.

Quantiles description
In statistics and probability quantiles are cut points dividing the range of a probability distribution into contiguous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one less quantile than the number of groups created. Thus quartiles are the three cut points that will divide a dataset into four equal-sized groups. Common quantiles have special names: for instance quartile, decile (creating 10 groups: see below for more). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points. * q-quantiles are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are q − 1 of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables. When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/q, 2/q, …, (q − 1)/q}.

Quantiles description

In statistics and probability quantiles are cut points dividing the range of a probability distribution into contiguous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one less quantile than the number of groups created. Thus quartiles are the three cut points that will divide a dataset into four equal-sized groups. Common quantiles have special names: for instance quartile, decile (creating 10 groups: see below for more). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.
* q-quantiles are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are q − 1 of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables. When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/q, 2/q, …, (q − 1)/q}.

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