weighted_mean_twod#

agabpylib.stats.moments.weighted_mean_twod(x, y, sx, sy, cxy)#

Provide the weighted mean of the vectors x and y.

The elements \((x_i, y_i)\) have covariance matrices:

\[\begin{split}\begin{pmatrix} s_x^2 & c_{xy}s_xs_y \\ c_{xy}s_xs_y & s_y^2 \end{pmatrix}\end{split}\]
Parameters:

  • x (float array (1D)) – Values of x-component of data vector

  • y (float array (1D)) – Values of y-component of data vector

  • sx (float array (1D)) – Uncertainties in x

  • sy (float array (1D)) – Uncertainties in y

  • cxy (float array (1D)) – Correlation coefficient of sx and sy

Returns:

  • wx, wy (float) – Weighted means wx, wy.

  • covw (float array (2,2)) – Covariance matrix of the weighted mean.