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Statistics

  

Percentile

  

compute percentiles

 

Calling Sequence

Parameters

Description

Options

Examples

References

Compatibility

Calling Sequence

Percentile(A, p, ds_options)

Percentile(X, p, rv_options)

Parameters

A

-

data set or Matrix data set

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

with(Statistics):

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

Percentile(Weibull(a, b), 30);

aln1071b

(1)

Use numeric parameters.

Percentile(Weibull(3, 5), 30);

3ln10715

(2)

Percentile(Weibull(3, 5), 30, numeric);

2.44104494075064

(3)

StandardError[10^5](Percentile, Weibull(3, 5), 30);

621100000007ln10745

(4)

StandardError[10^5](Percentile, Weibull(3, 5), 30, numeric);

0.00283364066608145

(5)

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

A := Sample(Weibull(3, 5), 10^5):

Percentile(A, 30);

2.44048423337317

(6)

StandardError[10^5](Percentile, A, 30);

0.00259397498616096428

(7)

Consider the following Matrix data set.

M := Matrix([[3,1130,114694],[4,1527,127368],[3,907,88464],[2,878,96484],[4,995,128007]]);

M31130114694415271273683907884642878964844995128007

(8)

We compute 29th percentile of each of the columns.

Percentile(M, 29);

2.88000000000000903.52000000000095521.6000000000

(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.

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[Quantile]

Statistics[RandomVariables]

Statistics[StandardError]