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Quantile

Quantile(list, q)

returns the q-Quantile of list.

Quantile(list, {q1, q2, ...})

returns a list of the q-Quantiles of list.

Quantile(list, q, {{a,b},{c,d}})

returns the q-Quantile of list with the quantile definition {{a,b},{c,d}}. The default parameters for the quantile definition are {{0,0},{1,0}}.

Common choices of parameters {{a,b},{c,d}} include:

  • {{0, 0}, {1, 0}} - inverse empirical CDF (default)

  • {{0, 0}, {0, 1}} - linear interpolation (California method)

In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. Quantile is also known as value at risk (VaR) or fractile.

See

Quantile can be applied to the following distributions:

BernoulliDistribution, ErlangDistribution, ExponentialDistribution, FrechetDistribution, GammaDistribution, GumbelDistribution, LogNormalDistribution, NakagamiDistribution, NormalDistribution, StudentTDistribution, WeibullDistribution

Examples

>> Quantile({1,2}, 0.5)
1


>> Quantile(NormalDistribution(m, s), q)
ConditionalExpression(m-Sqrt(2)*s*InverseErfc(2*q),0<=q<=1)


>> Quantile(Range(11), 1/3)
4


>> Quantile(Range(17), 1/4)
5


>> Quantile({1, 2, 3, 4, 5, 6, 7}, {1/4, 3/4})
{2,6}

FiveNum, Quartiles

Implementation status

  • ✅ - full supported

Github