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Copula
The resultant pattern of a scatter plot of data that helps to provide insight into the correlation (relationships) between different variables in a bi-variate or multi-variate matrix analysis.

That is, the intersection of two or more probability distributions or other types of distributions.




Application of copulas
Copulas can be used in the following ways within the domain of asset management:
  • To establish the strength of a relationship (if any) between two variables (say, age and condition)
  • To identify priorities for action.
  • To establish classes of buildings within a portfolio.
  • To assist in making resource allocation decisions
Copulas differ not so much in the degree of association they provide, but rather in which part of the distributions the association is strongest


Elements of a Copula
Listed below are some of the key elements in identifying the type of copula:
  • Slope (positive, negative or zero correlation)
  • Strength (Tails and tail concentrations - the degree of scatter)
  • Linearity (Linear vs. non-linear)
  • Right tail and left tail.
  • Clouds and dispersion.
  • Clusters and outliers.


Types of Copulas
Listed below are the five main types of copula patterns that have been identified in statistical science:


Analysis of the Copula
Listed below are some of the concepts to be used in analysis of a copula:
  • Copula gap
  • Copula front
  • Copula slope
  • Copula linearity
  • Copula trend line
  • Copula centre/Average point (see: Portfolio Average FCI)
  • Copula tail
  • Copula concentration/strength (degree of scatter)
  • Delta changes over time (see: Condition Drift)


Matrices
Listed below are some of the common matrices that are used to develop copulas in asset management:
A copula pattern can only be revealed if there are sufficient data points in the scatter plot.
Library of primary copula patterns on scatter plots
Fig. The five primary types of copulas each represented with positive slope/correlation.


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Fig. A Clayton copula with a long and concentrated left tail and positive slope/correlation.


The "high" performers identified on a scatter plotPoor performing buildings identified on a scatter plot
Fig.  Left: The "high" performers identified on a scatter plot. Right: The "poor" performers identified on a scatter plot. 


The leading edge (front)t of a copula indicating the data of the oldest buildings in a class
Fig. The leading edge (front) of a copula indicating the data of the oldest buildings in a class.




See also:
  • Statistics


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