Student[Statistics]
EmpiricalRandomVariable
Empirical random variable
Calling Sequence
Parameters
Description
Examples
References
Compatibility
EmpiricalRandomVariable(sample, opts)
sample
-
a list or rtable of samples
opts
(optional) an equation of the form probabilities = plist
The empirical random variable is a discrete probability distribution with probability function generated from the given sample.
If opts is not given, then Maple assigns a probability to each variate present within the sample equal to the fraction of occurrences of that value within the entire sample. If opts is specified, then plist should be a list or rtable of probabilities (nonnegative real numbers adding up to 1), having equally many entries as sample; the ith entry of plist specifies the probability for the ith entry of sample.
withStudentStatistics:
P≔1,1,1,2,2,2.5,3,4,4,5.5:
X≔EmpiricalRandomVariableP:
ProbabilityFunctionX,1
310
ProbabilityFunctionX,5
0
ProbabilityFunctionX,5.5
110
ProbabilityFunctionX,1,output=plot
CDFX,92
910
CDFX,x,output=plot
MeanX
2.60000000000000
VarianceX
2.090000000
Specify the probabilities.
M≔Matrix1,2,3,3.5,4,5
M≔1233.545
pmatrix≔Matrix115,215,515,415,115,215
pmatrix≔11521513415115215
Y≔EmpiricalRandomVariableM,probabilities=pmatrix:
ProbabilityFunctionY,x,output=plot
ProbabilityFunctionY,3.5
415
CDFY,x,output=plot
CDFY,4
1315
MedianY
3
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman, L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
The Student[Statistics][EmpiricalRandomVariable] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
Statistics[Distributions][EmpiricalDistribution]
Student
Student[Statistics][RandomVariable]
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