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Statistics

 Percentile
 compute percentiles

 Calling Sequence Percentile(A, p, ds_options) Percentile(X, p, rv_options)

Parameters

 A - X - algebraic; random variable or distribution p - algebraic; percentile ds_options - (optional) equation(s) of the form option=value where option is one of ignore, method, or weights; specify options for computing the percentile of a data set rv_options - (optional) equation of the form numeric=value; specifies options for computing the percentile of a random variable

Description

 • The Percentile function computes the specified percentile of the specified random variable or data set.
 • The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
 • The second parameter p is the percentile.

Options

 For a description of the available options, see the Statistics[Quantile] help page. Calling Percentile with percentile $p$ is equivalent to calling Quantile with probability $0.01p$.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

Compute the percentile of the Weibull distribution with parameters a and b.

 > $\mathrm{Percentile}\left(\mathrm{Weibull}\left(a,b\right),30\right)$
 ${a}{}{{\mathrm{ln}}{}\left(\frac{{10}}{{7}}\right)}^{\frac{{1}}{{b}}}$ (1)

Use numeric parameters.

 > $\mathrm{Percentile}\left(\mathrm{Weibull}\left(3,5\right),30\right)$
 ${3}{}{{\mathrm{ln}}{}\left(\frac{{10}}{{7}}\right)}^{{1}}{{5}}}$ (2)
 > $\mathrm{Percentile}\left(\mathrm{Weibull}\left(3,5\right),30,\mathrm{numeric}\right)$
 ${2.44104494075064}$ (3)
 > $\mathrm{StandardError}\left[{10}^{5}\right]\left(\mathrm{Percentile},\mathrm{Weibull}\left(3,5\right),30\right)$
 $\frac{{6}{}\sqrt{\frac{{21}}{{10000000}}}}{{7}{}{{\mathrm{ln}}{}\left(\frac{{10}}{{7}}\right)}^{{4}}{{5}}}}$ (4)
 > $\mathrm{StandardError}\left[{10}^{5}\right]\left(\mathrm{Percentile},\mathrm{Weibull}\left(3,5\right),30,\mathrm{numeric}\right)$
 ${0.00283364066608145}$ (5)

Generate a random sample of size 100000 drawn from the above distribution and compute the sample percentile.

 > $A≔\mathrm{Sample}\left(\mathrm{Weibull}\left(3,5\right),{10}^{5}\right):$
 > $\mathrm{Percentile}\left(A,30\right)$
 ${2.44048423337317}$ (6)
 > $\mathrm{StandardError}\left[{10}^{5}\right]\left(\mathrm{Percentile},A,30\right)$
 ${0.00259397498616096428}$ (7)

Consider the following Matrix data set.

 > $M≔\mathrm{Matrix}\left(\left[\left[3,1130,114694\right],\left[4,1527,127368\right],\left[3,907,88464\right],\left[2,878,96484\right],\left[4,995,128007\right]\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{3}& {1130}& {114694}\\ {4}& {1527}& {127368}\\ {3}& {907}& {88464}\\ {2}& {878}& {96484}\\ {4}& {995}& {128007}\end{array}\right]$ (8)

We compute 29th percentile of each of the columns.

 > $\mathrm{Percentile}\left(M,29\right)$
 $\left[\begin{array}{ccc}{2.88000000000000}& {903.520000000000}& {95521.6000000000}\end{array}\right]$ (9)

References

 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

 • The A parameter was updated in Maple 16.