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CC1/2: Difference between revisions
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→\sigma^2_{\epsilon}
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<math>s^2_{\epsilon_w}=\sum^N_{i} s^2_{\epsilon i\_w} / N </math> | <math>s^2_{\epsilon_w}=\sum^N_{i} s^2_{\epsilon i\_w} / N </math> | ||
It should be noted that it is not straightforward to define the correct way to calculate a weighted variance (and the weighted variance of the mean). The formula <math>s^2_w = \frac{n_{i}}{n_{i}-1} \cdot \left ( \frac{\sum^{n_{i}}_{j}w_{j,i} x^2_{j,i}}{\sum^{n_{i}}_{j}w_{j,i}} -\left ( \frac{ \sum^{n_{i}}_{j}w_{j,i}x_{j,i} }{\sum^{n_{i}}_{j}w_{j,i}}\right )^2 \right )</math> is - after some manipulation - the same as that found at [https://stats.stackexchange.com/questions/6534/how-do-i-calculate-a-weighted-standard-deviation-in-excel],[https://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf]. Other ways of calculating the weighted variance of the mean ([https://en.wikipedia.org/wiki/Weighted_arithmetic_mean]) should be considered. | It should be noted that it is not straightforward to define the correct way to calculate a weighted variance (and the weighted variance of the mean). The formula <math>s^2_w = \frac{n_{i}}{n_{i}-1} \cdot \left ( \frac{\sum^{n_{i}}_{j}w_{j,i} x^2_{j,i}}{\sum^{n_{i}}_{j}w_{j,i}} -\left ( \frac{ \sum^{n_{i}}_{j}w_{j,i}x_{j,i} }{\sum^{n_{i}}_{j}w_{j,i}}\right )^2 \right )</math> is - after some manipulation - the same as that found at [https://stats.stackexchange.com/questions/6534/how-do-i-calculate-a-weighted-standard-deviation-in-excel],[https://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf]. Other ways of calculating the weighted variance of the mean ([https://en.wikipedia.org/wiki/Weighted_arithmetic_mean],[https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html]) should be considered. | ||
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