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第515行： − 概率分布的概念及其描述的随机变量是概率论和统计学科学的数学基础。人口中几乎可以测量的任何值都存在价差或可变性（例如人的身高，金属的耐用性，销售增长，交通流量等）;几乎所有测量均存在一定的固有误差；在物理学中，从气体的动力学特性到基本粒子的量子力学描述，很多过程都用概率论来描述。由于这些以及许多其他原因，简单数字通常不足以描述数量，而概率分布通常更合适。+ − 以下是一些最常见的概率分布列表，按与之相关的过程类型进行分组。有关更完整的列表，请参见概率分布列表，该列表按要考虑的结果的性质（离散，连续，多元等）进行分组。+ − 下面所有的单变量分布都达到了峰值。也就是说，假设值聚集在单个点周围。实际上，实际观察到的量可能会聚集在多个值附近。可以使用混合物分布对此类数量进行建模。+ − + − + − + − + − + − + − + 第557行：
第557行： − + − +
→Common probability distributions and their applications 共同概率分布及其应用
The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory, and the science of statistics. There is spread or variability in almost any value that can be measured in a population (e.g. height of people, durability of a metal, sales growth, traffic flow, etc.); almost all measurements are made with some intrinsic error; in physics, many processes are described probabilistically, from the [[Kinetic theory of gases|kinetic properties of gases]] to the [[quantum mechanical]] description of [[fundamental particles]]. For these and many other reasons, simple [[number]]s are often inadequate for describing a quantity, while probability distributions are often more appropriate.
The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory, and the science of statistics. There is spread or variability in almost any value that can be measured in a population (e.g. height of people, durability of a metal, sales growth, traffic flow, etc.); almost all measurements are made with some intrinsic error; in physics, many processes are described probabilistically, from the [[Kinetic theory of gases|kinetic properties of gases]] to the [[quantum mechanical]] description of [[fundamental particles]]. For these and many other reasons, simple [[number]]s are often inadequate for describing a quantity, while probability distributions are often more appropriate.
概率分布和内蕴其中的随机变量的概念是概率论和统计学领域的基础。几乎任何可以在群体中测量的值都存在价差或可变性（例如人的身高，金属的耐用性，销售增长，交通流量等）;几乎所有测量都存在一定的固有误差；在物理学中，从气体动力学理论到基本粒子的量子力学描述都用概率论来描述。出于各种原因，简单数字通常很难表述一个量量，而用概率分布表述通常更合适。
The following is a list of some of the most common probability distributions, grouped by the type of process that they are related to. For a more complete list, see [[list of probability distributions]], which groups by the nature of the outcome being considered (discrete, continuous, multivariate, etc.)
The following is a list of some of the most common probability distributions, grouped by the type of process that they are related to. For a more complete list, see [[list of probability distributions]], which groups by the nature of the outcome being considered (discrete, continuous, multivariate, etc.)
以下列出了一些最常见的概率分布，按与之相关的过程类型进行分组。更完整的内容请参见概率分布列表，该列表按研究对象的性质（离散，连续，多元等）进行分组。
All of the univariate distributions below are singly peaked; that is, it is assumed that the values cluster around a single point. In practice, actually observed quantities may cluster around multiple values. Such quantities can be modeled using a [[mixture distribution]].
All of the univariate distributions below are singly peaked; that is, it is assumed that the values cluster around a single point. In practice, actually observed quantities may cluster around multiple values. Such quantities can be modeled using a [[mixture distribution]].
下面所有的单变量分布都是单峰的。也就是说，假设值聚集在单个值周围。实际上，实际观测量可能会聚集在多个值附近，可以使用混合分布对这种量进行建模。
=== '''<font color="#ff8000">Linear growth (e.g. errors, offsets) 线性增长 </font>'''===
=== '''<font color="#ff8000">Linear growth (e.g. errors, offsets) 线性增长 </font>'''===
* [[Normal distribution]] (Gaussian distribution), for a single such quantity; the most commonly used continuous distribution
* [[Normal distribution]] (Gaussian distribution), for a single such quantity; the most commonly used continuous distribution
'''<font color="#ff8000"> 正态分布（高斯分布 Normal Distribution</font>'''，对于单个这样的数量；最常用的连续分布
'''<font color="#ff8000"> 正态分布（高斯分布 Normal Distribution</font>'''，适用于单个变量；是最常用的连续分布
=== '''<font color="#ff8000"> Exponential growth (e.g. prices, incomes, populations) 指数增长</font>'''===
=== '''<font color="#ff8000"> Exponential growth (e.g. prices, incomes, populations) 指数增长</font>'''===
* [[Log-normal distribution]], for a single such quantity whose log is [[Normal distribution|normally]] distributed
* [[Log-normal distribution]], for a single such quantity whose log is [[Normal distribution|normally]] distributed
'''<font color="#ff8000">对数正态分布 Log-normal Distribution</font>'''，对于单个此类数量的对数正态分布
'''<font color="#ff8000">对数正态分布 Log-normal Distribution</font>'''，适用于对数为正态分布的单个变量
* [[Pareto distribution]], for a single such quantity whose log is [[Exponential distribution|exponentially]] distributed; the prototypical [[power law]] distribution
* [[Pareto distribution]], for a single such quantity whose log is [[Exponential distribution|exponentially]] distributed; the prototypical [[power law]] distribution
'''<font color="#ff8000">帕累托分布 Pareto Distribution</font>'''，对于单个这样的数量，其对数呈指数分布；原型幂律分布
'''<font color="#ff8000">帕累托分布 Pareto Distribution</font>'''，适用于指数为正态分布的单个变量；是幂律分布的原型
=== '''<font color="#ff8000"> Uniformly distributed quantities 数量均匀分布</font>'''===
=== '''<font color="#ff8000"> Uniformly distributed quantities 数量均匀分布</font>'''===
* [[Discrete uniform distribution]], for a finite set of values (e.g. the outcome of a fair die)
* [[Discrete uniform distribution]], for a finite set of values (e.g. the outcome of a fair die)
'''<font color="#ff8000"> 离散均匀分布 Discrete Uniform Distributed</font>'''，用于有限的一组值（例如，公平死亡的结果）
'''<font color="#ff8000"> 离散均匀分布 Discrete Uniform Distributed</font>'''，用于有限的一组值（例如，均匀骰子的结果）
* [[Continuous uniform distribution]], for continuously distributed values
* [[Continuous uniform distribution]], for continuously distributed values
'''<font color="#ff8000">连续均匀分布 Continuous Uniform Distributed</font>'''，用于连续分布的值
'''<font color="#ff8000">连续均匀分布 Continuous Uniform Distributed</font>'''，用于连续分布的值
=== Bernoulli trials (yes/no events, with a given probability) 伯努利试验（是/否事件，具有给定的概率）===
=== Bernoulli trials (yes/no events, with a given probability) 伯努利试验（给定的概率的是或否事件===
* Basic distributions 基本分布:
* Basic distributions 基本分布:
** [[Bernoulli distribution]], for the outcome of a single Bernoulli trial (e.g. success/failure, yes/no)
** [[Bernoulli distribution]], for the outcome of a single Bernoulli trial (e.g. success/failure, yes/no)
'''<font color="#ff8000"> 伯努利分布 Bernoulli Distribution</font>'''，用于单个伯努利试验的结果（例如成功/失败，是/否）
'''<font color="#ff8000"> 伯努利分布 Bernoulli Distribution</font>'''，用于描述单个伯努利试验的结果（例如成功/失败，是/否）
** [[Binomial distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed total number of [[Independent (statistics)|independent]] occurrences
** [[Binomial distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed total number of [[Independent (statistics)|independent]] occurrences
'''<font color="#ff8000">二项式分布 Binomial Distribution </font>'''，对于给定固定总数的独立“出现次数”（例如，成功，赞成票等）的数量
'''<font color="#ff8000">二项式分布 Binomial Distribution </font>'''，用于描述给定总数的前提下相互独立变量的成功次数（例如，成功，赞成票等）
** [[Negative binomial distribution]], for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs
** [[Negative binomial distribution]], for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs
** [[Geometric distribution]], for binomial-type observations but where the quantity of interest is the number of failures before the first success; a special case of the [[negative binomial distribution]]
** [[Geometric distribution]], for binomial-type observations but where the quantity of interest is the number of failures before the first success; a special case of the [[negative binomial distribution]]
'''<font color="#ff8000">几何分布 Geometric Distribution</font>'''，用于二项式观测，但是关注的数量是首次成功之前的失败数量；负二项式分布的特殊情况
'''<font color="#ff8000">几何分布 Geometric Distribution</font>'''，用于二项式观测，但是关注的数量是首次成功之前的失败数量；是负二项分布的特殊情况
* Related to sampling schemes over a finite population 与有限人口抽样方案有关:
* Related to sampling schemes over a finite population 与有限人口抽样方案有关:
** [[Hypergeometric distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed number of total occurrences, using [[sampling without replacement]]
** [[Hypergeometric distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed number of total occurrences, using [[sampling without replacement]]
'''<font color="#ff8000"> 超几何分布 Hypergeometric Distribution</font>'''，对于“肯定出现”的数量（例如成功，赞成票等），给定了一定的总出现数量，使用采样而无需替换
'''<font color="#ff8000"> 超几何分布 Hypergeometric Distribution</font>'''，描述“成功”的次数（例如成功，赞成票等），给定了一定的总出现数量，使用采样而无需替换
** [[Beta-binomial distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed number of total occurrences, sampling using a [[Pólya urn model]] (in some sense, the "opposite" of [[sampling without replacement]])
** [[Beta-binomial distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed number of total occurrences, sampling using a [[Pólya urn model]] (in some sense, the "opposite" of [[sampling without replacement]])