BUILT-IN MATHEMATICA SYMBOL
FindDistributionParameters
FindDistributionParameters[data, dist, {{p, p0}, {q, q0}, ...}]
finds the parameters p, q, ... with starting values 
, 
, ....
- 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:
-
- 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.
Obtain the maximum likelihood parameter estimates assuming a Laplace distribution:
| Out[1]= |  |
Obtain the method of moments estimates:
| Out[2]= |  |
Estimate parameters for a multivariate distribution:
| Out[2]= |  |
Compare the difference between the original and estimated PDFs:
| Out[3]= |  |
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