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→Relation to Zipf's law
是帕累托分布的。如果U在[0，1）上均匀分布，则可以与（1-U）交换。
是帕累托分布的。如果U在[0，1）上均匀分布，则可以与（1-U）交换。
===Relation to Zipf's law===
===Relation to Zipf's law与齐普夫定律的关系===
The Pareto distribution is a continuous probability distribution. [[Zipf's law]], also sometimes called the [[zeta distribution]], is a discrete distribution, separating the values into a simple ranking. Both are a simple power law with a negative exponent, scaled so that their cumulative distributions equal 1. Zipf's can be derived from the Pareto distribution if the <math>x</math> values (incomes) are binned into <math>N</math> ranks so that the number of people in each bin follows a 1/rank pattern. The distribution is normalized by defining <math>x_m</math> so that <math>\alpha x_\mathrm{m}^\alpha = \frac{1}{H(N,\alpha-1)}</math> where <math>H(N,\alpha-1)</math> is the [[Harmonic number#Generalized harmonic numbers|generalized harmonic number]]. This makes Zipf's probability density function derivable from Pareto's.
The Pareto distribution is a continuous probability distribution. [[Zipf's law]], also sometimes called the [[zeta distribution]], is a discrete distribution, separating the values into a simple ranking. Both are a simple power law with a negative exponent, scaled so that their cumulative distributions equal 1. Zipf's can be derived from the Pareto distribution if the <math>x</math> values (incomes) are binned into <math>N</math> ranks so that the number of people in each bin follows a 1/rank pattern. The distribution is normalized by defining <math>x_m</math> so that <math>\alpha x_\mathrm{m}^\alpha = \frac{1}{H(N,\alpha-1)}</math> where <math>H(N,\alpha-1)</math> is the [[Harmonic number#Generalized harmonic numbers|generalized harmonic number]]. This makes Zipf's probability density function derivable from Pareto's.
帕累托分布是一个连续的概率分布。[[Zipf定律]]，有时也称为[[zeta分布]]，是一个离散分布，将值分成一个简单的排名。它们都是一个简单的幂律，具有负指数，缩放后它们的累积分布等于1。如果将<math>x</math>值（收入）组合到<math>N</math>等级中，那么Zipf可以从Pareto分布中得出，这样每个箱子中的人数遵循1/rank模式。通过定义<math>xum</math>使<math>\alpha x\\mathrm{m}\alpha=\frac{1}{H（N，alpha-1）}</math>其中<math>H（N，alpha-1）</math>是[[调和数#广义调和数|广义调和数]]。齐夫函数的概率可由齐夫函数导出。
: <math>f(x) = \frac{\alpha x_\mathrm{m}^\alpha}{x^{\alpha+1}} = \frac{1}{x^s H(N,s)}</math>
: <math>f(x) = \frac{\alpha x_\mathrm{m}^\alpha}{x^{\alpha+1}} = \frac{1}{x^s H(N,s)}</math>
where <math>s = \alpha-1</math> and <math>x</math> is an integer representing rank from 1 to N where N is the highest income bracket. So a randomly selected person (or word, website link, or city) from a population (or language, internet, or country) has <math>f(x)</math> probability of ranking <math>x</math>.
where <math>s = \alpha-1</math> and <math>x</math> is an integer representing rank from 1 to N where N is the highest income bracket. So a randomly selected person (or word, website link, or city) from a population (or language, internet, or country) has <math>f(x)</math> probability of ranking <math>x</math>.
其中<math>s=\alpha-1</math>和<math>x</math>是一个整数，表示从1到N的等级，其中N是最高收入等级。因此，从某一人群（或语言、互联网或国家）中随机选择的人（或单词、网站链接或城市）具有<math>f（x）</math>排名概率<math>x</math>。
===Relation to the "Pareto principle"===
===Relation to the "Pareto principle"===