Multivariate Statistical Analysis of Indiana Hydrologic Data
Multivariate Statistical Analysis of Indiana Hydrologic Data
Multivariate Statistical Analysis of Indiana Hydrologic Data
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Copulas<br />
• Transformation <strong>of</strong> joint<br />
cumulative distribution<br />
– H XY(x,y) = C UV(u,v)<br />
marginals: u = F X(x), v = F Y(y)<br />
– Sklar (1959) proved that the<br />
transformation is unique for<br />
continuous r.v.s<br />
• Use copulas to construct joint<br />
distributions<br />
– Marginal distributions =><br />
selecting suitable PDFs<br />
– Dependence structure =><br />
selecting suitable copulas<br />
– Together they form the joint<br />
distribution
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