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Tail fitting, quantile interpolation [19]

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Bullet points include: Maybe we ‘know’ specific quantile values. E.g. because we trust expert judgement and these experts have for example identified the upper decile, median and lower decile of the distribution. If we have the same number of quantiles as we have parameters to fit then can use e.g. TWLS to fit quantiles exactly (if quantiles are feasible). E.g. lower quartile = -6, upper decile = +5 is fitted by N(-2.21, 5.62). Likewise if fewer quantiles and we fix sufficient numbers of distributional parameters. If we have more quantiles than we have available parameters then unlikely to get exact fit to all quantiles, but can select between possible ‘good’ alternatives by giving suitable weights to fit at different quantile points

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