Statistics - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Statistics and Data Analysis : Statistics Package : Quantities : Statistics/AbsoluteDeviation

Statistics

  

AbsoluteDeviation

  

compute the average absolute deviation from a given point

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

AbsoluteDeviation(A, b, ds_options)

AbsoluteDeviation(M, bs, ds_options)

AbsoluteDeviation(X, p, rv_options)

Parameters

A

-

data sample

M

-

Matrix

X

-

algebraic; random variable or distribution

b

-

real number; base point

bs

-

real number or list of real numbers; base points

p

-

algebraic expression; base point

ds_options

-

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

rv_options

-

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

Description

• 

The AbsoluteDeviation function computes the average absolute deviation of the specified random variable or data set from the specified base point.

• 

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

• 

The parameter b must be a real number in the first calling sequence. In the second calling sequence, M has to be a Matrix; then bs can be a real number or a list of real numbers. A list gives the base points for respective columns of the Matrix data set. If bs is a single real number, then the base point is the same for all columns. In the third calling sequence, p can be any expression of type/algebraic.

• 

If M is a DataFrame object, then b has to be a single real number as a base point.

Computation

• 

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.

• 

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

• 

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 AbsoluteDeviation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the AbsoluteDeviation 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 absolute deviation is computed symbolically. To compute the absolute deviation numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the average absolute deviation of the beta distribution with parameters 3 and 5 from point 12.

AbsoluteDeviation'Β'3,5,12

1751024

(1)

AbsoluteDeviation'Β'3,5,12,numeric

0.1708984375

(2)

Generate a random sample of size 100000 drawn from the above distribution and compute the sample absolute deviation from 12.

ASample'Β'3,5,105:

AbsoluteDeviationA,12

0.171666613743047

(3)

Compute the standard error of the sample absolute deviation from 12 for the normal distribution with parameters 5 and 2.

XRandomVariableNormal5,2:

BSampleX,106:

AbsoluteDeviationX,12,StandardError[106]AbsoluteDeviation,X,12

1242ⅇ8132+9πerf982π,120009742ⅇ8132+9πerf9822π

(4)

AbsoluteDeviationX,12,numeric,StandardError[106]AbsoluteDeviation,X,12,numeric

4.516938351,0.001961445368

(5)

AbsoluteDeviationB,12

4.51521003694514

(6)

Create a beta-distributed random variable Y and compute the average absolute deviation of 1Y+2 from 12.

YRandomVariable'Β'5,2:

AbsoluteDeviation1Y+2,12

1440ln2+5841440ln3

(7)

AbsoluteDeviation1Y+2,12,numeric

0.1302443242

(8)

Verify this using simulation.

CSample1Y+2,105:

AbsoluteDeviationC,12

0.130255483362204

(9)

Compute the average absolute deviation 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:

AbsoluteDeviationV,60,weights=W

HFloatundefined

(10)

AbsoluteDeviationV,60,weights=W,ignore=true

7.02737332556785

(11)

Consider the following Matrix data set.

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

M:=31130114694415271273683907884642878964844995128007

(12)

We compute the average absolute deviation from a fixed number.

AbsoluteDeviationM,10000

9996.800000000008912.600000000001.01003400000000105

(13)

It might be more useful to take the average absolute deviation from three different numbers.

AbsoluteDeviationM,3,1000,100000

0.600000000000000175.40000000000017024.2000000000

(14)

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 and bs parameters were 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]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam