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EllipsoidQuantile

Contributed by: Wolfram Research

Source Notebook

Find ellipsoidal location statistics

ResourceFunction["EllipsoidQuantile"][matrix,q]

gives the ellipsoidal locus of the qth quantile of matrix.

ResourceFunction["EllipsoidQuantile"][matrix,{q1,q2,}]

gives ellipsoidal loci for multiple quantiles q1,q2, ….

Details and Options

ResourceFunction["EllipsoidQuantile"][matrix,q] returns an Ellipsoid object centered at Mean[matrix].
The semi-axes radii are scaled to contain the fraction q of the sample space.
The value q can be any number between 0 and 1.

Examples

Basic Examples

Ellipsoidal quantile for bivariate data:

In[1]:=
ResourceFunction[
 "EllipsoidQuantile"][{{1, 3}, {2, 4}, {5, 6}, {7, 8}, {9, 10}}, .9]
Out[1]=

Scope

Multiple ellipsoidal quantiles for bivariate data:

In[2]:=
ResourceFunction[
 "EllipsoidQuantile"][{{1, 3}, {2, 4}, {5, 6}, {7, 8}, {9, 10}}, {.5, .9}]
Out[2]=

Applications

Visualize ellipsoidal quantiles for bivariate data:

In[3]:=
Show[Graphics /@ ResourceFunction[
   "EllipsoidQuantile"][{{1, 3}, {4, 4}, {5, 6}, {5, 15}, {20, 10}}, {.25, .5, .75, .9, .95}]]
Out[3]=

Resource History

See Also