MaximumLikelihoodFactory¶
- class MaximumLikelihoodFactory(*args)¶
Maximum likelihood factory.
- Parameters:
- distribution
Distribution
The parametric distribution .
- distribution
See also
Notes
This class implements the generic maximum likelihood estimation which is detailed in Maximum Likelihood Principle.
Let us denote the sample, the density of the parametric distribution we want to fit to the sample, with the parameter vector .
The likelihood of the sample according to is:
The log-likelihood is defined as:
The estimator of maximizes the log-likelihood:
Examples
In the following example, we estimate the parameters of a Normal distribution with maximum likelihood estimation.
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> distribution = ot.Normal(0.9, 1.7) >>> sample = distribution.getSample(10) >>> factory = ot.MaximumLikelihoodFactory(ot.Normal()) >>> inf_distribution = factory.build(sample)
Methods
BuildEstimator
(factory, sample[, isRegular])Estimate the parameters and the asymptotic distribution.
BuildGaussianEstimator
(distribution, sample)Compute the asymptotic distribution of the parameters.
build
(*args)Build the distribution.
buildEstimator
(*args)Build the distribution and the parameter distribution.
Accessor to the bootstrap size.
Accessor to the object's name.
Accessor to the known parameters indices.
Accessor to the known parameters indices.
getName
()Accessor to the object's name.
Accessor to the optimization solver.
Accessor to the optimization bounds.
hasName
()Test if the object is named.
setBootstrapSize
(bootstrapSize)Accessor to the bootstrap size.
setKnownParameter
(values, positions)Accessor to the known parameters.
setName
(name)Accessor to the object's name.
setOptimizationAlgorithm
(solver)Accessor to the optimization solver.
setOptimizationBounds
(optimizationBounds)Accessor to the optimization bounds.
Accessor to the optimization inequality constraint.
- __init__(*args)¶
- static BuildEstimator(factory, sample, isRegular=False)¶
Estimate the parameters and the asymptotic distribution.
- Parameters:
- factory
DistributionFactory
Distribution factory to infer the data
- sample2-d sequence of float
Data to infer
- is_regularbool
Indicates whether the parametric distribution is regular.
- factory
- Returns:
- result
DistributionFactoryResult
Result class providing the estimate and the asymptotic distribution.
- result
Notes
If the model is regular, the asymptotic distribution of the estimator is normal and we get it from the Delta method.
If the model is not regular, we use the Bootstrap method and the kernel smoothing method to get the asymptotic distribution of the estimator.
- static BuildGaussianEstimator(distribution, sample)¶
Compute the asymptotic distribution of the parameters.
- Parameters:
- distribution
Distribution
Parametric distribution.
- sample2-d sequence of float
Data to infer.
- distribution
- Returns:
- distribution
Normal
Asymptotic normal distribution of .
- distribution
Notes
We assume that the parametric model is regular: then, the asymptotic distribution of is normal.
- build(*args)¶
Build the distribution.
Available usages:
build()
build(sample)
build(param)
- Parameters:
- sample2-d sequence of float
Data.
- paramsequence of float
The parameters of the distribution.
- Returns:
- dist
Distribution
The estimated distribution.
In the first usage, the default native distribution is built.
- dist
- buildEstimator(*args)¶
Build the distribution and the parameter distribution.
- Parameters:
- sample2-d sequence of float
Data.
- parameters
DistributionParameters
Optional, the parametrization.
- Returns:
- resDist
DistributionFactoryResult
The results.
- resDist
Notes
According to the way the native parameters of the distribution are estimated, the parameters distribution differs:
Moments method: the asymptotic parameters distribution is normal and estimated by Bootstrap on the initial data;
Maximum likelihood method with a regular model: the asymptotic parameters distribution is normal and its covariance matrix is the inverse Fisher information matrix;
Other methods: the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting (see
KernelSmoothing
).
If another set of parameters is specified, the native parameters distribution is first estimated and the new distribution is determined from it:
if the native parameters distribution is normal and the transformation regular at the estimated parameters values: the asymptotic parameters distribution is normal and its covariance matrix determined from the inverse Fisher information matrix of the native parameters and the transformation;
in the other cases, the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting.
- getBootstrapSize()¶
Accessor to the bootstrap size.
- Returns:
- sizeint
Size of the bootstrap.
- getClassName()¶
Accessor to the object’s name.
- Returns:
- class_namestr
The object class name (object.__class__.__name__).
- getKnownParameterIndices()¶
Accessor to the known parameters indices.
- Returns:
- indices
Indices
Indices of the known parameters.
- indices
- getKnownParameterValues()¶
Accessor to the known parameters indices.
- Returns:
- values
Point
Values of known parameters.
- values
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getOptimizationAlgorithm()¶
Accessor to the optimization solver.
- Returns:
- solver
OptimizationAlgorithm
The solver used for the optimization of the log-likelihood.
- solver
- getOptimizationBounds()¶
Accessor to the optimization bounds.
- Returns:
- bounds
Interval
The bounds used for the optimization of the log-likelihood.
- bounds
- hasName()¶
Test if the object is named.
- Returns:
- hasNamebool
True if the name is not empty.
- setBootstrapSize(bootstrapSize)¶
Accessor to the bootstrap size.
- Parameters:
- sizeint
The size of the bootstrap.
- setKnownParameter(values, positions)¶
Accessor to the known parameters.
- Parameters:
- valuessequence of float
Values of known parameters.
- positionssequence of int
Indices of known parameters.
Examples
When a subset of the parameter vector is known, the other parameters only have to be estimated from data.
In the following example, we consider a sample and want to fit a
Beta
distribution. We assume that the and parameters are known beforehand. In this case, we set the third parameter (at index 2) to -1 and the fourth parameter (at index 3) to 1.>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> distribution = ot.Beta(2.3, 2.2, -1.0, 1.0) >>> sample = distribution.getSample(10) >>> factory = ot.MaximumLikelihoodFactory(ot.Beta()) >>> # set (a,b) out of (r, t, a, b) >>> factory.setKnownParameter([-1.0, 1.0], [2, 3]) >>> inf_distribution = factory.build(sample)
- setName(name)¶
Accessor to the object’s name.
- Parameters:
- namestr
The name of the object.
- setOptimizationAlgorithm(solver)¶
Accessor to the optimization solver.
- Parameters:
- solver
OptimizationAlgorithm
The solver used for the optimization of the log-likelihood.
- solver
Examples using the class¶
Fit a distribution by maximum likelihood
Fitting a distribution with customized maximum likelihood