StandardWeightedCubicQuantileFit
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Function Description
Returns an array corresponding to a weighted cubic curve fit
to observed quantile values, where the weights correspond to the distance
between consecutive points (so that the fit gives greater weight to the tails
of the distribution). Requires as inputs an ordered array of values
(e.g. expected quantiles, as per MnStandardisedNormalQuantiles
and an ordered array of values
corresponding to the actually observed values.
The curve fit is derived using the Nematrian least squares
generalised curve fit MnLeastSquaresGeneralisedCurveFit,
(specifically the polynomial
version).
The weights, , used in
this function, if the ordered values are and there
are such
values, are:
This potentially under allows for the two end points. An
alternative that gives greater weight to the two end points is MnStandardWeightedCubicQuantileFitInclEnds.
Please bear in mind that a cubic is not always a valid form
for a quantilequantile function to take (e.g. if the slope of the cubic
becomes negative anywhere). If you wish to avoid this problem then we suggest
fitting a distributional form using e.g. (weighted) maximum likelihood, see
e.g. MnProbDistWeightedMLE.
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