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BUILT-IN MATHEMATICA SYMBOL
ParameterEstimator
ParameterEstimator
is an option to EstimatedDistribution and FindDistributionParameters that specifies what parameter estimator to use.
Details
- The following basic settings can be used:
-
"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 will 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 
. - The different methods of moments include:
, 
, 
, or 
. - With ParameterEstimator->{mm, "MomentOrders"->list}, the moment orders specified by list are used for the method of moments estimator mm.
- For univariate distributions, the moment orders should be a list of positive integers.
- For
-dimensional distributions, the moment orders should be length 
lists of non-negative integers with each list summing to a positive number. - ParameterEstimator->{"estimator", Method->"solver"} specifies what underlying equation or optimization solver to use.
- Possible solver settings for
include: -
Automatic automatically chosen solver "FindMaximum" use FindMaximum to maximize log-likelihood "FindRoot" use FindRoot to solve likelihood equations "NMaximize" use NMaximize to maximize log-likelihood - Possible solver settings for
, 
, 
, and 
include: -
Automatic automatically chosen solver "FindRoot" use FindRoot to solve moment equations "NSolve" use NSolve to solve moment equations "Solve" use Solve to solve moment equations - The Automatic setting uses a solver or combination of solvers based on the distribution and the parameters to be estimated.
- With the setting ParameterEstimator->{"estimator", Method->{"solver", opts}}, additional options can be given for the solver.
- Solver methods such as Solve, NSolve, and NMaximize that do not rely on starting values will not make use of starting values given to EstimatedDistribution or FindDistributionParameters.
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