EVT and alternatives [15]

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Bullet points include: EVT seems very helpful. Characterises limiting distributions very succinctly. But requires regularity conditions that may not be satisfied. Relies on existence of a limiting distribution but this is not guaranteed. At issue is potential unreliability of extrapolation. E.g. Press et al. (2007). Assume limiting distribution of tail is fat-tailed GPD. Thus use approximation: Problem of estimating F and its (tail) quantiles then reduces to problem of estimating mu, sigma and xi for the approximating generalised Pareto distribution. 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 form of curve fitting approach. E.g. polynomial curve fit such as a cubic (see earlier), as long as the resulting extrapolation is credible

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