LeastSquaresDistributionFactory¶
- class LeastSquaresDistributionFactory(*args)¶
Least squares factory.
- Parameters:
- distribution
Distribution
The distribution defining the parametric model to be adjusted to data.
- distribution
See also
Notes
The method fits a scalar distribution to data of dimension 1, using a least-squares minimization method.
Let us denote the sample, the cumulative distribution function we want to fit to the sample, and its parameter vector.
let denote the empirical cumulative distribution function built from the sample.
The estimator minimizes the mean square error between and on the empirical quantiles.It is defined as:
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> distribution = ot.Normal(0.9, 1.7) >>> sample = distribution.getSample(10) >>> factory = ot.LeastSquaresDistributionFactory(ot.Normal()) >>> inf_distribution = factory.build(sample)
Methods
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 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 solver.
setOptimizationBounds
(optimizationBounds)Accessor to the optimization bounds.
Accessor to the optimization inequality constraint.
- __init__(*args)¶
- 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 fixed parameters.
- indices
- getKnownParameterValues()¶
Accessor to the known parameters indices.
- Returns:
- values
Point
Values of fixed parameters.
- values
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getOptimizationAlgorithm()¶
Accessor to the solver.
- Returns:
- solver
OptimizationAlgorithm
The solver used for numerical optimization of the likelihood.
- solver
- getOptimizationBounds()¶
Accessor to the optimization bounds.
- Returns:
- problem
Interval
The bounds used for numerical optimization of the likelihood.
- problem
- 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 fixed parameters.
- indicessequence of int
Indices of fixed parameters.
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> distribution = ot.Beta(2.3, 4.5, -1.0, 1.0) >>> sample = distribution.getSample(10) >>> factory = ot.LeastSquaresDistributionFactory(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 solver.
- Parameters:
- solver
OptimizationAlgorithm
The solver used for numerical optimization of the likelihood.
- solver