The Sample command generates a random sample drawn from the distribution given by X.

The first parameter, X, can be a random variable, or an algebraic expression involving random variables (see Student[Statistics][RandomVariable]).

The second parameter, n, is the sample size. The function will return a newly created Vector of length n, filled with the sample values.

If the option output is not included or is specified to be output=value, then the function will return the generated sample as a Vector. If output=plot is specified, then the function will return a density plot of the input random variable together with a histogram of the sample. If output=both is specified, then both the value and the plot will be returned.

If X is a continuous random variable, or an expression that contains a floating point value, or an expression that contains a continuous random variable, then the sample is returned as floating point values. Otherwise, the sample is returned as exact values.

By default, the data are generated according to the rule above. To always generate data numerically, specify the numeric or numeric=true option.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right)\:$

$X≔\mathrm{NormalRandomVariable}\left(0\,1\right)$

$X≔\mathrm{\_R}$

$A≔\mathrm{Sample}\left(X\,10\right)$

$A≔\left[\begin{array}{cccccccccc}\mathrm{-1.07242412799827}& \mathrm{-0.329077870547065}& \mathrm{-0.617091936909790}& 0.214466745245291& \mathrm{-0.0254281280423846}& 1.72882128417783& \mathrm{-1.63485675434390}& 1.57117217175430& 0.170358421410408& 1.00647840875181\end{array}\right]$

$\mathrm{Sample}\left(X\,{10}^5\,\mathrm{output}=\mathrm{plot}\right)$

$Y≔\mathrm{NormalRandomVariable}\left(0\,1\right)$

$Y≔\mathrm{\_R0}$

$\mathrm{Sample}\left(\exp \left(X\right)Y\,10\right)$

$\left[\begin{array}{cccccccccc}3.26573974537506& \mathrm{-1.13201372396577}& 0.377102787673808& \mathrm{-0.466881079873879}& \mathrm{-0.919968549940460}& 0.618766627953613& 1.21251674537321& 0.209692542612765& \mathrm{-0.353909479087286}& \mathrm{-0.190908459890482}\end{array}\right]$

$B≔\mathrm{PoissonRandomVariable}\left(3\right)$

$B≔\mathrm{\_R1}$

$\mathrm{Sample}\left(\frac{B}{\mathrm{\pi }}\,10\right)$

$\left[\begin{array}{cccccccccc}\frac{2}{\mathrm{\pi }}& \frac{4}{\mathrm{\pi }}& \frac{3}{\mathrm{\pi }}& 0& \frac{3}{\mathrm{\pi }}& \frac{1}{\mathrm{\pi }}& \frac{2}{\mathrm{\pi }}& 0& \frac{5}{\mathrm{\pi }}& \frac{3}{\mathrm{\pi }}\end{array}\right]$

$\mathrm{Sample}\left(\frac{B}{\mathrm{\pi }}\,10\,\mathrm{numeric}\right)$

$\left[\begin{array}{cccccccccc}1.59154943091895& 0.954929658551372& 0.954929658551372& 2.22816920328654& 0.318309886183791& 1.27323954473516& 0.954929658551372& 0.954929658551372& 0.954929658551372& 0.636619772367581\end{array}\right]$

$\mathrm{dataset},\mathrm{graph}≔\mathrm{Sample}\left(B\,100\,\mathrm{output}=\mathrm{both}\right)$

$\mathrm{dataset},\mathrm{graph}≔\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}3& 6& 2& 5& 2& 3& 0& 7& 2& 1& 3& 1& 2& 5& 4& 3& 2& 5& 3& 5& 1& 2& 2& 4& 3& 4& 4& 4& 2& 7& 2& 1& 1& 4& 1& 2& 0& 3& 1& 1& 3& 0& 5& 5& 2& 4& 6& 4& 4& 4& 3& 2& 1& 1& 2& 3& 1& 1& 3& 3& 2& 4& 2& 2& 2& 2& 5& 3& 2& 1& 3& 3& 0& 3& 2& 0& 3& 2& 5& 3& 0& 4& 5& 1& 2& 3& 2& 5& 3& 3& 5& 2& 2& 5& 5& 1& 8& 4& 4& 3\end{array}\right],\mathrm{PLOT}\left(\mathrm{...}\right)$

$\mathrm{dataset}$

$\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}3& 6& 2& 5& 2& 3& 0& 7& 2& 1& 3& 1& 2& 5& 4& 3& 2& 5& 3& 5& 1& 2& 2& 4& 3& 4& 4& 4& 2& 7& 2& 1& 1& 4& 1& 2& 0& 3& 1& 1& 3& 0& 5& 5& 2& 4& 6& 4& 4& 4& 3& 2& 1& 1& 2& 3& 1& 1& 3& 3& 2& 4& 2& 2& 2& 2& 5& 3& 2& 1& 3& 3& 0& 3& 2& 0& 3& 2& 5& 3& 0& 4& 5& 1& 2& 3& 2& 5& 3& 3& 5& 2& 2& 5& 5& 1& 8& 4& 4& 3\end{array}\right]$

$\mathrm{graph}$

$C≔\mathrm{Sample}\left(X^2\,{10}^4\right)$

$\mathrm{Mean}\left(C\right)$

$0.994862958212511$

$\mathrm{Median}\left(C\right)$

$0.455147477689335$

$\mathrm{Skewness}\left(C\right)$

$2.81421618454522$

$\mathrm{Kurtosis}\left(C\right)$

$14.8537269935385$

$\mathrm{Variance}\left(C\right)$

$1.96550597257815$

$\mathrm{StandardDeviation}\left(C\right)$

$1.40196503971324$

$\mathrm{Quantile}\left(C\,0.6\right)$

$0.713125222514264$

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

Walker, Alastair J. New Fast Method for Generating Discrete Random Numbers with Arbitrary Frequency Distributions, Electronic Letters, 10, 127-128.

Walker, Alastair J. An Efficient Method for Generating Discrete Random Variables with General Distributions, ACM Trans. Math. Software, 3, 253-256.

The Student[Statistics][Sample] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.