BUILT-IN MATHEMATICA SYMBOL

# FindDistributionParameters

FindDistributionParameters[data, dist]
finds the parameter estimates for the distribution dist from data.

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

## Details and OptionsDetails and Options

• FindDistributionParameters returns a list of replacement rules for the parameters in dist.
• 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:
•  AccuracyGoal Automatic the accuracy sought ParameterEstimator "MaximumLikelihood" what parameter estimator to use PrecisionGoal Automatic the precision sought WorkingPrecision Automatic the 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 sample moment and is the 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 Laplace distribution:

 Out[1]=

Obtain the method of moments estimates:

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Estimate parameters for a multivariate distribution:

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Compare the difference between the original and estimated PDFs:

 Out[3]=