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Statistics

  

HarmonicMean

  

compute the harmonic mean

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

HarmonicMean(A, ds_options)

HarmonicMean(M, ds_options)

HarmonicMean(X, rv_options)

Parameters

A

-

data sample

M

-

Matrix data set

X

-

algebraic; random variable or distribution

ds_options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the mean of a data set

rv_options

-

(optional) equation of the form numeric=value; specifies options for computing the mean of a random variable

Description

• 

The HarmonicMean function computes the harmonic mean of the specified random variable or data set.

• 

The first parameter can be a data set (given as 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]).

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

All computations involving data are performed in floating-point; therefore, all data provided must have type/realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Data Set Options

  

The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.

• 

ignore=truefalse -- This option controls how missing data is handled by the HarmonicMean command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the HarmonicMean command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

• 

weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight 1.

Random Variable Options

  

The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the mean is computed using exact arithmetic. To compute the mean numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the mean of the beta distribution with parameters p and q.

HarmonicMean'Β'p,q

Βp,qΓp+q1ΓqΓ1+p

(1)

Use numeric parameters.

HarmonicMeanUniform3,5

112ln3+12ln5

(2)

HarmonicMeanUniform3,5,numeric

3.915230378

(3)

Generate a random sample of size 1000 drawn from the above distribution and compute the sample mean.

ASampleUniform3,5,103:

HarmonicMeanA

3.89308555036164

(4)

Create a beta-distributed random variable Y and compute the mean of 1Y+2.

YRandomVariable'Β'5,2:

HarmonicMean1Y+2

719

(5)

HarmonicMean1Y+2,numeric

0.3684210526

(6)

Verify this using simulation.

CSample1Y+2,103:

HarmonicMeanC

0.367743892525739

(7)

Compute the mean of a weighted data set.

Vseqi,i=57..77,undefined:

W2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:

Digits40

Digits:=40

(8)

HarmonicMeanV,weights=W

Floatundefined

(9)

HarmonicMeanV,weights=W,ignore=true

66.92176161684632539311650421092512741624

(10)

Digits10:

Consider the following Matrix data set.

MMatrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M:=31130114694415271273683907884642878964844995128007

(11)

We compute the harmonic mean of each of the columns.

HarmonicMeanM

3.000000000000001044.637851394491.08576132666248105

(12)

References

  

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

Compatibility

• 

The M parameter was introduced in Maple 16.

• 

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

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[ExpectedValue]

Statistics[RandomVariables]

Statistics[StandardError]

 


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