VonMisesFactory

(Source code, png)

../../_images/openturns-VonMisesFactory-1.png
class VonMisesFactory(*args)

VonMises factory.

Parameters:
circularbool, optional

Flag to tell if the data are in \Rset (circular=False) or in \Rset/(2\pi\Zset) (circular=True). Default is True.

See also

DistributionFactory, VonMises

Notes

If circular=True, we introduce z_n=\frac{1}{n}\sum_{k=1}^ne^{iX_k}. Then, the estimators read:

\begin{eqnarray*} \displaystyle\Hat{\mu}_n^{\strut} &=& \mathrm{Arg}(z_n)\\ \displaystyle\Hat{\kappa}_n&\mbox{s.t.}&\frac{I_1(\Hat{\kappa}_n)}{I_0(\Hat{\kappa}_n)}=\sqrt{\frac{n}{n-1}\left(|z_n|^2-\frac{1}{n}\right)} \end{eqnarray*}

where I_0 and I_1 are the modified Bessel functions of the first kind of order 0 and 1.

If circular=False, the estimators read:

\begin{eqnarray*} \displaystyle\Hat{\mu}_n^{\strut}&=&\frac{1}{n}\sum_{k=1}^n X_k\\ \displaystyle\Hat{\kappa}_n&\mbox{s.t.}&\frac{I_1(\Hat{\kappa}_n)}{I_0(\Hat{\kappa}_n)}=\frac{1}{n}\sum_{k=1}^n\cos(X_k-\Hat{\mu}_n) \end{eqnarray*}

Note that the last equation has no solution if the right-hand side is not positive.

In both cases, the resolution of this equation defininig \Hat{\kappa}_n can be tuned through VonMisesFactory-RelativePrecision, VonMisesFactory-ResidualPrecision, VonMisesFactory-MaximumIteration in ResourceMap

Methods

build(*args)

Build the distribution.

buildAsVonMises(*args)

Build the VonMises distribution.

buildEstimator(*args)

Build the distribution and the parameter distribution.

getBootstrapSize()

Accessor to the bootstrap size.

getClassName()

Accessor to the object's name.

getId()

Accessor to the object's id.

getName()

Accessor to the object's name.

getShadowedId()

Accessor to the object's shadowed id.

getVisibility()

Accessor to the object's visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

setBootstrapSize(bootstrapSize)

Accessor to the bootstrap size.

setName(name)

Accessor to the object's name.

setShadowedId(id)

Accessor to the object's shadowed id.

setVisibility(visible)

Accessor to the object's visibility state.
__init__(*args)
build(*args)

Build the distribution.

Available usages:

build(sample)

build(param)

Parameters:
sample2-d sequence of float

Sample from which the distribution parameters are estimated.

paramCollection of PointWithDescription

A vector of parameters of the distribution.

Returns:
distDistribution

The built distribution.

buildAsVonMises(*args)

Build the VonMises distribution.

Available usages:

buildAsVonMises(sample)

buildAsVonMises(param)

Parameters:
sample2-d sequence of float

Sample from which the distribution parameters are estimated.

paramCollection of PointWithDescription

A vector of parameters of the distribution.

Returns:
distVonMises

The built distribution.

buildEstimator(*args)

Build the distribution and the parameter distribution.

Parameters:
sample2-d sequence of float

Sample from which the distribution parameters are estimated.

parametersDistributionParameters

Optional, the parametrization.

Returns:
resDistDistributionFactoryResult

The results.

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:
sizeinteger

Size of the bootstrap.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns:
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:
hasVisibleNamebool

True if the name is not empty and not the default one.

setBootstrapSize(bootstrapSize)

Accessor to the bootstrap size.

Parameters:
sizeinteger

Size of the bootstrap.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.