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Tail fitting, quantile interpolation [10]

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Bullet points include: In traditional EVT we assume that the limiting distribution of observations in the tail of the distribution is a generalised Pareto distribution (GPD). Problem of estimating distribution and hence behaviour in the tail (e.g. tail quantiles) then in effect reduces to problem of estimating from the data the parameters that provide the best fit GPD to the data. Can be done using mean excess functions, maximum likelihood (ML) estimation, method of moments etc. But equally we could fit to the relevant part of the QQ-plot using any other reasonable curve fitting approach. As long as the fit is feasible, does it have to tend to a GPD in the limit?

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