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第138行：
第138行： − − − || \left[\frac x \sigma \right]^{-\alpha} − − [ frac x sigma right ] ^ {-alpha } 第184行：
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→Related distributions相关分布
===Generalized Pareto distributions广义帕累托分布===
===Generalized Pareto distributions广义帕累托分布===
There is a hierarchy <ref name=arnold/><ref name=jkb94>Johnson, Kotz, and Balakrishnan (1994), (20.4).</ref> of Pareto distributions known as Pareto Type I, II, III, IV, and Feller–Pareto distributions.<ref name=arnold/><ref name=jkb94/><ref name=kk03>{{cite book |author1=Christian Kleiber |author2=Samuel Kotz |lastauthoramp=yes |year=2003 |title=Statistical Size Distributions in Economics and Actuarial Sciences |publisher=[[John Wiley & Sons|Wiley]] |isbn=978-0-471-15064-0|ref=harv| url=https://books.google.com/books?id=7wLGjyB128IC}}</ref> Pareto Type IV contains Pareto Type I–III as special cases. The Feller–Pareto<ref name=jkb94/><ref name=feller>{{cite book|last=Feller |first= W.| year=1971| title=An Introduction to Probability Theory and its Applications| volume=II| edition=2nd | location= New York|publisher=Wiley|page=50}} "The densities (4.3) are sometimes called after the economist ''Pareto''. It was thought (rather naïvely from a modern statistical standpoint) that income distributions should have a tail with a density ~ ''Ax''<sup>−''α''</sup> as ''x'' → ∞."</ref> distribution generalizes Pareto Type IV.
There is a hierarchy <ref name=arnold/><ref name=jkb94>Johnson, Kotz, and Balakrishnan (1994), (20.4).</ref> of Pareto distributions known as Pareto Type I, II, III, IV, and Feller–Pareto distributions.<ref name=arnold/><ref name=jkb94/><ref name=kk03>{{cite book |author1=Christian Kleiber |author2=Samuel Kotz |lastauthoramp=yes |year=2003 |title=Statistical Size Distributions in Economics and Actuarial Sciences |publisher=[[John Wiley & Sons|Wiley]] |isbn=978-0-471-15064-0|ref=harv| url=https://books.google.com/books?id=7wLGjyB128IC}}</ref> Pareto Type IV contains Pareto Type I–III as special cases. The Feller–Pareto<ref name=jkb94/><ref name=feller>{{cite book|last=Feller |first= W.| year=1971| title=An Introduction to Probability Theory and its Applications| volume=II| edition=2nd | location= New York|publisher=Wiley|page=50}} "The densities (4.3) are sometimes called after the economist ''Pareto''. It was thought (rather naïvely from a modern statistical standpoint) that income distributions should have a tail with a density ~ ''Ax''<sup>−''α''</sup> as ''x'' → ∞."</ref> distribution generalizes Pareto Type IV.
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