freealg.distributions.DeformedMarchenkoPastur.support

DeformedMarchenkoPastur.support(eta=0.0002, n_probe=4000, thr=0.0005, x_max=None, x_pad=0.05, method='quartic')

Support intervals of distribution

Parameters:

etafloat, default=2e-4

Imaginary offset used in the Stieltjes inversion for density.

n_probeint, default=4000

Number of grid points used to probe the density (when applicable).

thrfloat, default=5e-4

Density threshold used to detect nonzero regions (when applicable).

x_maxfloat or None, default=None

Optional right endpoint for probing-based methods.

x_padfloat, default=0.05

Optional padding used for search/probing range.

method{'quartic', 'probe'}, default=``’quartic’``

Method used to estimate the support.

Returns:

intervalslist of tuple(float, float)

List of (left, right) support intervals.

See also

density

Notes

Estimate support intervals of \(\mu = H \boxtimes \mathrm{MP}_c\) where \(H = \sum_i w_i \delta_{t_i}\).

Examples

>>> from freealg.distributions import DeformedMarchenkoPastur
>>> dmp = DeformedMarchenkoPastur(t=[2.0, 5.5], w=[0.75, 1-0.75],
...     c=0.1)

>>> print(dmp.support)
[(1.271942644768898, 2.796717409578293),
 (4.465954791747979, 6.910028011047688)]