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Statistics

  

Likelihood

  

compute likelihood function of a random variable and data set

 

Calling Sequence

Parameters

Description

Options

Examples

Compatibility

Calling Sequence

Likelihood(R, V, options)

Parameters

R

-

algebraic; a random variable or distribution

V

-

name or rtable; data sample

options

-

(optional) equation(s) of the form option=value where option is one of samplesize, ignore, normalize, or weights; specify options for the Likelihood function

Description

• 

The Likelihood function computes the likelihood function of a random variable R evaluated on a data set V.

• 

The first parameter R can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

• 

The second parameter V can be an Array of data samples or a symbol representing an Array of data samples (in which case the option samplesize must be specified).

Options

  

The options argument can contain one or more of the options shown below.

• 

samplesize=deduce or posint -- If this option is set to 'deduce' (default) the likelihood function attempts to automatically determine the number of data samples provided in V.  This parameter must be specified if the number of samples in V is not immediately detectable.

• 

ignore=truefalse -- This option is used to specify how to handle non-numeric data. If ignore is set to true all non-numeric items in V will be ignored.

• 

normalize=truefalse -- This option selects whether factors that do not depend on the value of the parameters can be omitted. The default is normalize = true, meaning that such factors can be omitted; selecting normalize = false means they are included.

• 

weights=rtable -- Vector of weights (one-dimensional rtable). If weights are given, the Likelihood function will scale each data point to have given weight. Note that the weights provided must have type realcons and the results are floating-point, even if the problem is specified with exact values. Both the data array and the weights array must have the same number of elements.

Examples

withStatistics:

Calculate the general likelihood function from the Normal distribution.

LikelihoodNormalμ,σ,A,samplesize=4

ⅇA1μ22σ2ⅇA2μ22σ2ⅇA3μ22σ2ⅇA4μ22σ2σ4

(1)

Sample a random variable with Normal distribution.

NRandomVariableNormal5,1:

SSampleN,4:

Attempt to compute the likelihood function of this sample.

LikelihoodNormalμ,1,S

ⅇ4.52065806636344μ22ⅇ5.78417369973330μ22ⅇ4.49951342516818μ22ⅇ4.50894910106650μ22

(2)

If we want to get a measure of the likelihood of some fully specified normal distributions for a given sample, we need to include the normalize=false. Otherwise, since there are no parameters in the distribution, all factors are omitted and we always get the answer 1.

LikelihoodNormal5.0,1.0,S,LikelihoodNormal4.8,1.2,S

1,1

(3)

LikelihoodNormal5.0,1.0,S,'normalize=false',LikelihoodNormal4.8,1.2,S,'normalize=false'

0.0129856344759522,0.00799276640176335

(4)

Insert missing data into the array and recompute.

S4undefined:

LikelihoodNormalμ,1,S

ⅇ4.52065806636344μ22ⅇ5.78417369973330μ22ⅇ4.49951342516818μ22ⅇFloatundefinedμ22

(5)

LikelihoodNormalμ,1,S,ignore=true

ⅇ4.52065806636344μ22ⅇ5.78417369973330μ22ⅇ4.49951342516818μ22

(6)

Consider a weighted structure.

SSampleN,4:

W2,2,0,0:

LikelihoodNormalμ,1,S,weights=W

ⅇ5.23782835292544μ222ⅇ4.85175935951542μ222

(7)

Compatibility

• 

The V parameter was updated in Maple 16.

• 

The normalize option was introduced in Maple 16.

• 

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

See Also

Statistics

Statistics[Computation]