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Weighted Importance in sampled data statistics

  1. Nov 4, 2012 #1
    I was just wondering how exactly to appropriately modify the 1st and 2nd order stats when you want to weight a given sample more heavily. If [itex] \vec{X} [/itex] is my vector of N samples and I have a weight vector [itex] \vec{W} [/itex] of the same dimension, which ideally is measuring the reliability of each sample from 0 to 1. Could I calculate mean and variance using...

    [itex]
    \vec{Y}_i= \vec{X}_i\vec{W}_i
    \\

    \mu_{x-weighted} = E[\vec{Y}]
    \\

    \sigma_{x-weighted} = E[(\vec{Y}-E[\vec{Y}])^2]
    \\

    [/itex]

    Let me know what you think. Thanks.

    EDIT: [itex] \LaTeX [/itex] mods...
     
  2. jcsd
  3. Nov 4, 2012 #2
    The weighted mean is given by...

    [tex]\mu_w = \frac{\sum x_iw_i}{\sum w_i}[/tex]

    The weighted sample variance is...

    [tex]\sigma^2_w = \frac{\sum w_i(x_i - \mu_w)^2}{\sum w_i}[/tex]
     
  4. Nov 4, 2012 #3
    Hey thanks!
     
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