Estimation Commands - Maple Help

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Estimation Commands

  

The Statistics package supports a variety of tools for manipulating likelihood functions, performing maximum likelihood estimation and deriving various properties of the likelihood function.

 

Available Commands

Examples

Available Commands

FisherInformation

Fisher information

Information

statistical information

KernelDensity

estimate the probability density of a data set

Likelihood

likelihood function

LikelihoodRatioStatistic

compute the likelihood ratio statistic

LogLikelihood

log likelihood function

MaximumLikelihoodEstimate

compute the maximum likelihood estimate

Score

statistical score

Examples

withStatistics:

Calculate the likelihood, log likelihood and score function of a beta distribution

Likelihood'Β'a,b,A,samplesize=1

&lcub;0A1<0A11&plus;a1A1b1&Beta;a&comma;bA1<101A1

(1)

LogLikelihood&apos;&Beta;&apos;a&comma;b&comma;A&comma;samplesize&equals;1

lnA11&plus;a1A1b1&Beta;a&comma;b

(2)

Score&apos;&Beta;&apos;a&comma;b&comma;A&comma;samplesize&equals;1

lnA1&Psi;a&plus;&Psi;a&plus;bln1A1&Psi;b&plus;&Psi;a&plus;b

(3)

Attempt to calculate the maximum likelihood estimate of a binomial distribution.

SSampleBinomial10&comma;0.4&comma;1000

S:= 1 .. 1000 VectorrowData Type: float8Storage: rectangularOrder: Fortran_order

(4)

MaximumLikelihoodEstimateBinomial10&comma;&theta;&comma;S&comma;bounds&equals;0..1

0.393699998407612

(5)

Calculate the same information about a normal distribution.

assume0<&sigma;

InformationNormal&mu;&comma;&sigma;&comma;A&comma;samplesize&equals;1&comma;param&equals;&mu;

1&sigma;~2

(6)

FisherInformationNormal&mu;&comma;&sigma;&comma;1&comma;&mu;

1&sigma;~2

(7)

Compute the likelihood ratio statistic about a similar normal distribution.

LikelihoodRatioStatisticNormal&mu;&comma;5&comma;A&comma;samplesize&equals;1

125A12225A1&mu;&plus;125&mu;2

(8)

See Also

Statistics

Statistics[Computation]

 


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