Copula Parameter Estimator
Copula Parameter Estimator estimates the correlation parameter \\( \rho \\) of a Gaussian copula from paired data \\( (u_i, v_i) \\). Enter data as semicolon-separated pairs (e.g., “0.2,0.3;0.4,0.5”). The calculator uses maximum likelihood estimation (MLE) to compute \\( \rho \\). Results are visualized as a scatter plot with p5.js, and computational steps are displayed with MathJax.
Copula Parameter Estimator
This calculator estimates the correlation parameter \\( \rho \\) of a Gaussian copula \\( C(u, v; \rho) = \Phi_\rho(\Phi^{-1}(u), \Phi^{-1}(v)) \\) using maximum likelihood estimation (MLE). Input paired data \\( (u_i, v_i) \\) as semicolon-separated pairs (e.g., “0.2,0.3;0.4,0.5”), where \\( u_i, v_i \in [0,1] \\), and the number of optimization steps. Results are visualized as a scatter plot using p5.js, and steps are shown with MathJax. Share or embed results as needed.
Example 1: Positively Correlated Data
Data: “0.1,0.2;0.3,0.4;0.6,0.5;0.8,0.7”, Steps: 100.
Result: \\( \rho \approx 0.9 \\).
Example 2: Negatively Correlated Data
Data: “0.2,0.8;0.3,0.7;0.5,0.4;0.8,0.2”, Steps: 100.
Result: \\( \rho \approx -0.9 \\).
Example 3: Independent Data
Data: “0.1,0.3;0.4,0.6;0.5,0.4;0.7,0.8”, Steps: 100.
Result: \\( \rho \approx 0 \\).