WeightedPercentile
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Function Description
Returns ,
the m’th weighted percentile ( here being between 0 and
1) of a series of observations series given
weights (for
).
Different commentators use different ways of identifying
percentiles (i.e. quantiles) from finite sized samples. See MnPercentile and MnPercentileExc for
details of how the Nematrian website calculates equallyweighted percentiles,
which match the approaches used by Microsoft.
For weighted percentiles, the Nematrian website uses
the following approach, which is not fully compatible with the approach it uses
for unweighted percentiles:

First sort the series in ascending order

Next build up a cumulative distribution based on the weights, and assume
that the percentile points for the midpoints of each bin are the in
question (so, if the weight of the first in the ordered list is then
the ’th
percentile is deemed to be exactly ,
the ’th percentile is deemed
to be exactly ,
etc.)

Finally use linear interpolation as per the MnLinearInterpolation
function to interpolate remaining percentiles.
The MnLinearInterpolation
function does not extrapolate beyond the minimum and maximum values, so the
0’th and 1’th quantiles should be the minimum and maximum values of the series,
and hence be consistent with what would be returned for these quantile values
by the MnPercentile
function. However, intermediate values with the all
equal will not correspond exactly to those that would be returned by the MnPercentile function.
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