satlas.utilities.utilities.weighted_average¶

satlas.utilities.utilities.weighted_average(x, sigma, axis=None)[source]¶

Takes the weighted average of an array of values and the associated errors. Calculates the scatter and statistical error, and returns the greater of these two values.

Parameters:	x (array_like) – Array-like assortment of measured values, is transformed into a 1D-array. sigma (array_like) – Array-like assortment of errors on the measured values, is transformed into a 1D-array.
Returns:	Returns a tuple (weighted_average, uncertainty), with the uncertainty being the greater of the uncertainty calculated from the statistical uncertainty and the scattering uncertainty.
Return type:	tuple

Note

The formulas used are

$\left\langle x\right\rangle_{weighted} &= \frac{\sum_{i=1}^N \frac{x_i} {\sigma_i^2}} {\sum_{i=1}^N \frac{1} {\sigma_i^2}} \sigma_{stat}^2 &= \frac{1}{\sum_{i=1}^N \frac{1}{\sigma_i^2}} \sigma_{scatter}^2 &= \frac{\sum_{i=1}^N \left(\frac{x_i-\left\langle x\right\rangle_{weighted}} {\sigma_i}\right)^2} {\left(N-1\right)\sum_{i=1}^N \frac{1}{\sigma_i^2}}$

satlas.utilities.utilities.weighted_average¶

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