Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 EllipsoidQuantile

Source Notebook

Find ellipsoidal location statistics

Contributed by: Wolfram Research

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 (1) 

Ellipsoidal quantile for bivariate data:

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

Scope (1) 

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 (1) 

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]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

  • 1.0.0 – 19 February 2019

Related Resources

License Information