概率论与数理统计常用英文词汇对照
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Jul 17, 2021
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Jul 17, 2021 12:28 PM
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概率论与数理统计常用英文词汇对照
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Math
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Field
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Probability Theory 概率论
Trial 试验
intersection 交
union 并
frequency 频率
difference 差
additivity 可加性
complementation 对立
contain 包含
equivalent 等价
mean 均值
convolution [,kɔnvə’lu:ʃən] 卷积
variance 方差
covariance 协方差
correlated 相关
standard deviation 标准差
Random experiment 随机试验
random event 随机事件
certain event 必然事件
impossible event 不可能事件
elementary/fundamental event 基本事件
the probability of event A 事件的概率
sample point 样本点
sample space 样本空间
Classical probability 古典概型
geometric probability 几何概型
conditional probability 条件概型
total probability 全概率
formula of multiplication 乘法公式
pair wise independence 两两相互独立
Distribution function 分布函数
discrete random variable 离散型随机变量
two-point distribution （0-1）分布
binomial distribution 二次分布
Poisson distribution 泊松分布
hyper geometric distribution 超几何分布
Continuous random variable 连续型随机变量
probability density function 概率密度函数
uniform distribution 均匀分布
Exponential distribution 指数分布
standard normal distribution 标准正态分布
Cauchy distribution 柯西分布
n-dimensional random vector n 维随机变量
bivariate random variable [bai’vεəriət] 二维随机变量
joint distribution function 联合分布函数
bivariate discrete random variable 二维离散型随机变量
joint distribution law 联合分布律
bivariate continuous random variable 二维连续型随机变量
joint probability density function 联合概率密度函数
bivariate normal distribution 二维正态分布
marginal distribution function 边缘分布函数
marginal distribution law 边缘分布律
marginal probability density function 边缘概率密度函数
conditional distribution function 条件分布函数
conditional probability density function 条件概率密度函数
mathematical expectation 数学期望
standard random variable 标准随机变量
moment generating function 矩母函数
characteristic function 特征函数
positive correlated 正相关
mixed moment 混合矩
negative correlated 负相关
mixed central moment 混合中心矩
moment of order k about the origin 阶原点矩
central moment of order k 阶中心矩
covariance matrix 协方差矩阵
convergence in probability 依概率收敛
Bernouli large numbers law 伯努力大数定律
Mathematical statistics 数理统计
individuality 个体
population 总体
sample size 样本大小
simple random sample 随机样本
efficiency 有效
statistic 统计量
sample mean 样本均值
sample variance 样本方差
sample standard deviation 样本标准差
sample central moment of order k 样本的阶中心矩
skewness [’skju:nis] 偏度
coefficient of variation 变异系数
order statistics 次序统计量
degrees or freedom 自由度
sampling distribution 抽样分布
parameter estimation 参数估计
point estimation 点估计
estimator 估计量
estimate 估计值
likelihood function 似然函数
method of moment 矩估计法
unbiased estimator 无偏估计量
maximum likelihood estimate 最大似然估计
system of likelihood equations 似然方程组
consistent estimator 一致估计量
confidence level 置信水平
confidence interval 置信区间
upper confidence limit 置信上限
parametric hypothesis 参数估计
non-parametric hypothesis 非参数估计
alternative hypothesis 备择假设
null hypothesis 零假设
Significance level 显著性水平
rejection region 拒绝域
acceptance region 接受域
test for goodness of fit 拟和优度检验
contingency table 列连表
regression function 回归函数
regression equation 回归方程
linear regression model 线形回归模型
regression coefficient 回归系数
normal linear model 正态线形模型
least squares estimate 最小二乘估计
method of least squares 最小二乘法
sum of squares of residual 残差平方和
sum of squares of regression 回归平方和
sum of residual 剩余平方和
total sum of squares of deviations 总变差平方和
coefficient of determination 判定系数
point interval 点预测
prediction interval 预测区间
one-way analysis variance 单因素方差分析
two-way analysis of variance 双因素方差分析
interaction effect 交互效应 > 本文由简悦 SimpRead 转码
- 总共有 r 种可能性：overall there are r possibilities for the whole experiment
- 关于。。。的假设：assumptions about。。
- 在。。的假设下：under various assumptions
- 如何收集样本：how the samples are collected
- n 中采样 k 个：gives the number of possible samples of size k out of a population of size n
- 有序，无序：order matters，not matter
- 有放回，无放回：with replacement，without replacement
- 如果所有的结果是等可能的，则事件 A 发生的概率为：If all outcomes are equally likely, the probability of an event A happening is.
- A 是否发生与 B 是否发生无关：whether A occurred gives no information about whether B occurred
- 独立事件：independent events
- 条件独立：conditional independence
- A 与 B 独立当且仅当下面等价命题成立：A and B are independent if and only if one of the following equivalent statements holds.
- A 与 B 在 C 下是条件独立的：A and B are conditionally independent given C
- 条件独立并不意味着独立：conditional independence does not imply independence
- 并，交，补：union，intersection，complements
- 德摩根定律：De Morgan’s Laws，将并（交）的计算转化为交（并）的等式：A identity that can make caculating probabilities of unions easier by relating them to intersections, and vice versa.
- 辛普森悖论：Simpson’s Paradox
- 全概率定理：Law of Total Probability
- 贝叶斯法则：Bayes’ Rule
- 联合概率，边际概率，条件概率：joint probability, marginal probability, conditional probability
- 所有适用于概率的定理也适用于条件概率：Any theorem that holds for probability also holds for conditional probability
- 样本空间的一个分割：a partition of the sample space
- 他们是不相交的：they are disjoint
- 他们的并是整个样本空间：their union is the entir sample space
- 特例：special case
- 我们还可以写成：we can also write
- A 的后验是似然比乘先验：The posterior odds of A are the likelihood ratio times the prior odds.
- 概率质量函数：probability mass function
- 概率密度函数：probability density function
- 累积分布函数：cumulative distribution function
- 给定一个离散变量在取得某一值的概率：gives the probability that a discrete random variable takes on the value x.
- a 满足：a satisfies
- 一个随机变量小于等于 x：a random variable is less than or equal to x.
- CDF 是递增的，右连续的函数，且：CDF is an increasing, right-continuous function with…
- 一个与另一个无关：one gives no information about the other.
- 期望：expected value，mean，expectation，average
- 加权平均：weighted average
- 正式的，公式化的，数学上的, 更一般地：more formally，mathematically, more generally
- 常数：constants
- 相同的分布意味着相同的均值：same distribution means same mean
- 在事件 A 下：conditioned on event A
- 如果事件发生，指示为 1，否则为 0：if the event occurs, the indicator is 1; otherwise it is 0.
- 在一个区间：in an interval
- 差：difference
- 。。。的导数：the derivative of …
- 非负且和为 1：A PDF is nonnegative and integrates to 1.
- 依据微积分的基本定理：by the fundamental theorem of calculus
- 随机变量在一定区间内的值：CRV takes on a value in an interval
- 将这一区间上的 PDF 累积：integrate the PDF over that interval
- 累加 x 乘 PMF（离散）：sum x times the PMF
- 累加 x 乘 PDF（连续）：integrate x times the PDF
- X 的期望定义如下：the expected value of X is defined this way:
- 也是：is also
- 万流归宗：universality of Uniform （plug a CRV into its own CDF, get a Uniform(0, 1)）
- 无意识统计学家定律：The Law of Unconscious Statistician
- 将 x 替换成 X：plug X into x
- 让 X 的均值为 mu，标准差为 sigma：Let X have mean mu and standard deviation sigma.
- 均值，方差，偏差，峰值：mean，variance，skewness，kurtosis
- 泰勒展开式：Taylor expansion
- 他们分布相同：They are distributed the same
- 之和，之积：the sum of 。。 the product of。。
- 在离散 / 连续情况：in the discrete/continuous case
- 联合分布，条件分布，边际分布：joint distribution, conditional…, maginal …
- 当且仅当下列条件满足：if and only if any of the following conditions holds
- 表示：denote
- 与。。相似：be analogous to ..
- 。。的近似：the analog of …
- 属于 - 1,1：between-1 and 1
- 相反情况不一定对：the converse is not necessarily right
- X,Y 是独立同分布的：X, Y are identically distributed
- 对于任意常数 a，b 且 a，b 补位零：for any constants a, b with a and b nonzero
- 位置不变的，尺度不变的：location-invariant, scale-invariant
- 函数 g 是可微分的，严格递增的：the function g is differentiable and strictly increasing(decreasing)
- 雅克比，雅克比矩阵：Jacobian, Jacobian matrix
- 矩阵的行列式：the determinant of the matrix/ matrix’s determinant
- 卷积积分：convolution integral
- 两个独立随机变量 X，Y 之和：the sum of two independent CRVs X and Y
- 独立同分布：i.i.d.
- 泊松过程：Poisson Process
- 每单位时间 x 到达：x arrivals per unit time
- 在长度为 t 的时间间隔内：in a time interval of length t
- 不相交的时间间隔：disjoint time interval
- 二元性，对偶性：duality
- 顺序统计量：order statistics
- 将他们从最小到最大排列：arrange them from smallest to largest
- 10 次独立伯努利实验：10 independent Bernoulli trials
- 假设：given that
- 无记忆性属性：memoryless property
- 在前三次实验中：among the first 3 trails
- 亚当定律：Adam’s Law a.k.a. Law of Total Expectation
- Eve’s Law: a.k.a. Law of Total Variance
- 大数定律：Law of Large Numbers
- 中心极限定理：Central Limit Theorem
- 样本均值：sample mean
- 收敛至：converge to。。
- 近似分布的：approximately distributed
- 换句话说：in other words
- X is distributed 。。
- 连续分布：continuous distribution
- 均匀分布：Uniform Distribution
- 指数分布: Exponential Distribution
- gamma 分布：Gamma Distribution
- β分布：Beta distribution
- 二项分布的共轭先验：conjugate prior of Binomial
- 卡方分布：Chi-Square distribution
- 离散分布：discrete distribution
- 二项分布：Binomial
- 伯努利分布：Bernoulli..
- 几何分布：Geometric..
- 一次成功分布：First Success..
- 负二项分布：Negative Binomial ..
- 超几何分布：Hypergemetric ..
- 泊松分布：Poisson ..
- 多元分布：multivariant..
- 多项式分布：Multinomial
- 多元高斯分布：multivariant normal …
- 多元均匀分布：multivariant uniform…
- 公式：formulas
- 几何级数、等比级数：geometric series
- 积分：integrals
- 调和：Harmonic
- 欧拉逼近：Euler’s approximation
- 阶乘的 Stirling 逼近：Stirling’s approximation > 本文由简悦 SimpRead 转码