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Statistics[Distributions]

  

EmpiricalDistribution

  

Empirical distribution

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

EmpiricalDistribution(sample, opts)

Parameters

sample

-

a list or rtable of samples

opts

-

(optional) an equation of the form probabilities = plist

Description

• 

The empirical distribution 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.

• 

If all the values in sample are positive integers, you can use the ProbabilityTable distribution instead.

• 

Note that the EmpiricalDistribution command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics:

PArray1,1,1,2,4,4,5.5:

XRandomVariableEmpiricalDistributionP:

ProbabilityFunctionX,1

37

(1)

ProbabilityFunctionX,5

0

(2)

ProbabilityFunctionX,5.5

17

(3)

CDFX,4

67

(4)

MeanX

2.64285714285714

(5)

VarianceX

2.908163265

(6)

YRandomVariableEmpiricalDistribution1,2.5,4,5,'probabilities'=13,14,1360,15

Y:=_R0

(7)

ProbabilityFunctionY,52

14

(8)

CDFY,4.5

0.8000000000

(9)

MedianY

52

(10)

TallySampleY,106

5.=199920,1.=332622,4.=216982,2.50000000000000=250476

(11)

References

  

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.

Compatibility

• 

The probabilities option was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]

 


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