EstimatedDistribution[data, dist]
estimates the parametric distribution dist from data.

EstimatedDistribution[data, dist, {{p, p0}, {q, q0}, ...}]
estimates the parameters p, q, ... with starting values , , ....

Details and OptionsDetails and Options

  • EstimatedDistribution returns the symbolic distribution dist with parameter estimates inserted for any non-numeric values.
  • The data must be a list of possible outcomes from the given distribution dist.
  • The distribution dist can be any parametric univariate, multivariate, or meta distribution with unknown parameters.
  • The following options can be given:
  • AccuracyGoalAutomaticthe accuracy sought
    ParameterEstimator"MaximumLikelihood"what parameter estimator to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecisionAutomaticthe precision used in internal computations
  • The following basic settings can be used for ParameterEstimator:
  • "MaximumLikelihood"maximize the log-likelihood function
    "MethodOfMoments"match raw moments
    "MethodOfCentralMoments"match central moments
    "MethodOfCumulants"match cumulants
    "MethodOfFactorialMoments"match factorial moments
  • The maximum likelihood method attempts to maximize the log-likelihood function , where are the distribution parameters and is the PDF of the symbolic distribution.
  • The method of moments solves , , ..., where is the ^(th) sample moment and is the ^(th) moment of the distribution, with parameters .
  • Method-of-moment-based estimators may not satisfy all restrictions on parameters.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

Obtain the maximum likelihood parameter estimates, assuming a gamma distribution:

Click for copyable input
Click for copyable input

Visually compare the PDFs for the original and estimated distributions:

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Obtain the method of moments estimates:

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Estimate parameters for a multivariate distribution:

Click for copyable input
Click for copyable input
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