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, σ
2).
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
σ
2 = αβ
2
exponential probability distribution 指數機率分布
chi-square distribution 卡方分布 (χ
2)
degrees of freedom 自由度 v or n or df
Special cases of gamma distribution:
exponential distribution => α = 1
μ = β
σ
2 = β
2
chi-square distribution => α = v/2, n/2 or df/2, β = 2
μ = v or n (degrees of freedom)
σ
2 = 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
