Probability Distribution Terms 機率分布名詞

random variable 隨機變數
sample space 樣本空間 S

probability distribution 機率分布/機率分配
sampling distribution 抽樣分布

normal population 常態母體

statistic 統計量
sample statistic 樣本統計量
sample mean 樣本平均數

sample variance 樣本變異數 

discrete probability distribution 離散機率分布
probability mass function (pmf) 機率質量函數
probability function 機率函數

continuous probability distribution 連續機率分布
probability density function (pdf) 機率密度函數 - total area under pdf curve = 1
density function 密度函數
continuous uniform distribution 連續均勻分布

cumulative distribution function (cdf) 累積分布函數 - 離散及連續皆有cdf

expected value/expectation 期望值
conditional expectation 條件期望值

uniform probability distribution 均勻機率分布
normal probability distribution 常態機率分布/常態機率分配 N(μ,σ²)
normal distribution 常態分布 / Gaussian distribution 高斯分布
standard normal probability distribution 標準常態機率分布 N(0,1) (mean μ = 0 and variance σ² = 1)

Z-score/Z-value/Z-transform/standard score z分數/z轉換/標準化值 (Wikipedia/維基百科)
How to get the Z-tansform from normal random variable X:
Z = (X - μ)/σ where μ = population mean and σ = populaiton variance

Z 是N(0,1) 的標準常態分布

(Note: The Z-transform used in statistics is not the Z-transform used is digital signal processing. 此處的Z轉換與數位訊號處理DSP中的Z轉換不同)

normal probability distribution 常態機率分布 can be represented as N(μ, σ²).
standard normal probability distribution 標準常態機率分布 can be represented as N(0, 1).

binomial probability distribution 二項機率分布
Bernoulli 柏努利/白努力/貝努力
moment-generating function 動差生成函數/力矩產生函數

negative binomial distribution 負二項分布
geometric distribution 幾何分布
hypergeometric distribution 超幾何分布

Poisson probability distribution 卜瓦松機率分布
Poisson approximation 卜瓦松近似/瓦松近似逼近

Log-normal distribution 對數常態分布

gamma probability distribution 伽瑪機率分布 (uppercase gamma character: Γ)
Two parameters:
α - shape parameter
β - scale parameter

μ = αβ
σ² = αβ²

exponential probability distribution 指數機率分布
chi-square distribution 卡方分布 (χ²)
degrees of freedom 自由度 v or n or df

Special cases of gamma distribution:
exponential distribution => α = 1
μ = β
σ² = β²

chi-square distribution => α = v/2, n/2 or df/2, β = 2
μ = v or n (degrees of freedom)
σ² = 2v or 2n

Erlang distribution 厄朗分布/厄蘭分布/艾朗分布

Beta distribution 貝他分布

joint probability distribution 聯合機率分布
joint probability mass function (joint pmf) 聯合機率質量函數 (discrete X and Y random variables)
joint probability density function (joint pdf) 聯合機率密度函數 (continuous X and Y random variables)

marginal distribution 邊際分布

conditional probability distribution 條件機率分布

bivariate distribution 二元分布/二變量分布/雙變數分布

Student t-distribution/Student's t-distribution 學生t分布
t-distribution t分布

Weibull distribution 威布爾分布/韋布林分布/韋氏分布/魏普分布

參考資料

Mathematical statistics with applications in R, Ramachandran & Tsokos, 2nd edition (2015)
Essentials of Probability & Statistics for Engineers & Scientists (Walpole at el.)，機率與統計 (繆紹綱譯，滄海2013)，p155, p174-181
國家教育研究院雙語詞彙、學術名詞暨辭書資訊網
機率與統計：動差生成函數 (Moment Generation Function) (陳鍾誠網站)
Wikipedia