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Nematrian Reference Library

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Abstract "In this paper we introduce four ways of estimating probability distribution parameters that target a good fit to a user selected part of the distributional form (e.g. one or both tails). We analyse the characteristics of the resulting parameter estimates for a wide range of commonly used probability distributions. Three of the methodologies reviewed are similar, are motivated by maximum likelihood principles and give the same results as traditional (unweighted) maximum likelihood estimation in the special case where all quantiles within the distributional form are given equal weight. The fourth methodology involves a direct weighted least squares fit to a suitable quantile-quantile plot."

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