# Changeset 744 for trunk/doc/Statistics.tex

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Timestamp:
Feb 10, 2007, 9:16:11 PM (15 years ago)
Message:

corrected some typos

File:
1 edited

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 r675 % 02111-1307, USA. \usepackage{html} {\bf Weighted Statistics} \normalsize \begin{htmlonly} This document is also available in \htmladdnormallink{PDF}{Statistics.pdf}. \end{htmlonly} \tableofcontents have not chosen one situation for our implementations, so see specific function documentation for what assumtions are made. Though, common for implementationare the following: for implementations are the following: \begin{itemize} \item Setting all weights to unity yields the same result as the \sigma^2=-^2= \\\frac{\sum w_ix_i^2}{\sum w_i}-\frac{(\sum w_ix_i)^2}{(\sum w_i)^2}= \\\frac{\sum w_i(x_i^2-m^2)}{\sum w_i} \\\frac{\sum w_i(x_i^2-2mx_i+m^2)}{\sum w_i} \\\frac{\sum w_i(x_i^2-m^2)}{\sum w_i}= \\\frac{\sum w_i(x_i^2-2mx_i+m^2)}{\sum w_i}= \\\frac{\sum w_i(x_i-m)^2}{\sum w_i} \end{eqnarray} This estimator fulfills that it is invariant under a rescaling and having a weight equal to zero is equivalent to removing the data point. Having all weight equal to unity we get $\sigma=\frac{\sum point. Having all weights equal to unity we get$\sigma=\frac{\sum (x_i-m)^2}{N}\$, which is the same as returned from Averager. Hence, this estimator is slightly biased, but still very efficient.