non-parametric-continuous-cumulative-distribution

schema/objects/non-parametric-continuous-cumulative-distribution/1.1.0/non-parametric-continuous-cumulative-distribution.schema.json

The non-parametric-continuous-cumulative-distribution object captures the statistical cumulative distribution function (CDF) of a property. It is non-parametric since the CDF is not characterized by a known distribution (e.g., normal or lognormal) or by a mathematical formula. Instead, the cumulative probability is calculated directly from the data and from an extrapolation function if the data does not capture the full range of possible values.

This schema is particularly useful in geostatistics where the distribution of properties such as mineral grades, porosity, or seismic velocities may not follow a known distribution. This object is beneficial for geostatistical conditional simulations, change of support analysis and other methods that typically assume Gaussianity, though natural data is rarely follow a Gaussian distribution. Techniques like declustering and Gaussian anamorphosis help manage these distributions, where Gaussian anamorphosis does not assume a predefined distribution, but instead, it derives a transformation function from the empirical (non-parametric) CDF, ensuring a data-driven approach.

To create this object, the user must provide:

• The pairs of values and probabilities. Note that the values are sorted and the probabilities should be monotonically increasing between 0 and 1 (excluded).
• The lower tail extension; use No_extrapolation if the lowest value is also the minimum of the distribution.
• The upper tail extension; use No_extrapolation if the largest value is also the maximum of the distribution.
• Note the support of the distribution. Select Point or specify a block size.
• Specify if the distribution has been declustered.

Properties

non-parametric-continuous-cumulative-distribution (v1.2.0)

A description of a non parametric continuous cumulative distribution.

Property	Type	Description	Flags
name	String	Name of the object.	⬆️ ✅
uuid	base-object-properties	Identifier of the object.	⬆️ ✅
description	String	Optional field for adding additional description to uniquely identify this object.	⬆️
extensions	Object	Extended properties that may be associated to the object, but not specified in the schema	⬆️
tags	Object	Key-value pairs of user-defined metadata	⬆️
lineage	lineage	Information about the history of the object	⬆️
bounding_box	bounding-box	Bounding box of the spatial data.	⬆️ ✅
coordinate_reference_system	crs	Coordinate system of the spatial data	⬆️ ✅
schema	String		✅
cdf	cumulative-distribution-function	Cumulative distribution function.	✅
is_declustered	Boolean	Is declustered.	✅
support	non-parametric-continuous-cumulative-distribution	Support options.	✅
attribute_description	attribute-description	The attribute description record.

Legend

Flag	Description
⬆️	Inherited property
✅	Required property