Simulation Commands
The Statistics package provides optimized algorithms for simulating from all supported distributions as well as tools for creating custom random number generators, parametric and non-parametric bootstrap.
Bootstrap
compute bootstrap statistics
KernelDensitySample
sample a kernel density estimate
Sample
generate random sample
Examples
with⁡Statistics:
Generate random sample drawn from the non-central beta distribution.
X≔RandomVariable⁡NonCentralBeta⁡3,10,2:
A≔Sample⁡X,1000
Use the bootstrap to estimate the mean and the standard error of the mean.
Bootstrap⁡Mean,X,replications=1000,output=value,standarderror
0.282229356166131,0.00399644288773034952
Bootstrap⁡Mean,A,replications=1000,output=value,standarderror
0.275083017014237,0.00384426186874453797
Compare this with analytic results.
Mean⁡X
−1762148409+4790016000⁢ⅇ−1
evalf30⁡Mean⁡X
0.28226746351970438745
Mean⁡X,numeric
0.2822674635
Random sample involving two independent random variables.
Y≔RandomVariable⁡Cauchy⁡0,1
Y≔_R0
Z≔RandomVariable⁡Cauchy⁡1,2
Z≔_R1
B≔Sample⁡Y2+Z2,105
See Also
Statistics
Statistics[Computation]
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