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Tail fitting, quantile interpolation [13]

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Bullet points include: One possible alternative is simply to fit a curve, e.g. a polynomial, directly to the relevant tail of the observed QQ-plot, selecting its coefficients using e.g. weighted least squares, to target the best fit within the tail. But this does not always return a feasible probability distribution and may be difficult to interpret. Probably better is to use ‘tail weighted’ approaches, e.g. tail weighted least squares or tail weighted maximum likelihood, see Kemp (2013). Implemented via web functions named “MnProbDistTW…” in the Nematrian function library. Always returns a feasible probability distribution, as the ‘best fit’ (in the tail) is automatically constrained to fall within a specified family of valid distributions. Maximum likelihood variant inherits the nice asymptotic properties of maximum likelihood estimation and if equally weight fit across whole distribution then same as traditional MLE

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