卜瓦松分布 | Poisson distribution mean
![卜瓦松分布](https://i.imgur.com/axBPWDg.jpg)
卜瓦松分布機率質量函數橫軸是索引k,發生次數。該函數只定義在k為整數的時候。連接線是只為了指導視覺。累積分布函數橫軸是索引k,發生次數。CDF在整數k處不連續,且在其他任何地方都是水平的,因為服從卜瓦松分布的變數只針對整數值。母數λ>0(實數)值域k∈{0,1,2,3,⋯}{displaystylekin{0,1,2,3,cdots}}機率質量函數λkk!e−λ{displaystyle{frac{lambda{k}}{k!}}e{-lambda}}累積分布函數Γ(⌊k+1⌋,λ)⌊k⌋!{displaystyle{frac{Gamma(lfloork+1floor,lambda)}{lfloorkfloor!}}},或e−λ∑i=0⌊k⌋λii! {displaystylee{-lambda}sum_{i=0}{lfl...
![卜瓦松分布](https://i.imgur.com/H8YKUrg.jpg)
機率質量函數
橫軸是索引k,發生次數。該函數只定義在k為整數的時候。連接線是只為了指導視覺。累積分布函數
橫軸是索引k,發生次數。CDF在整數k處不連續,且在其他任何地方都是水平的,因為服從卜瓦松分布的變數只針對整數值。母數 λ > 0(實數)值域 k∈{0,1,2,3,⋯}{displaystyle kin {0,1,2,3,cdots }}機率質量函數 λkk!e−λ{displaystyle {frac {lambda {k}}{k!}}e{-lambda }}累積分布函數Γ(⌊k+1⌋,λ)⌊k⌋!{displaystyle {frac {Gamma (lfloor k+1 floor ,lambda )}{lfloor k floor !}}},或e−λ∑i=0⌊k⌋λii! {displaystyle e{-lambda }sum _{i=0}{lfloor k floor }{frac {lambda {i}}{i!}} },或Q(⌊k+1⌋,λ){displaystyle Q(lfloor k+1 floor ,lambda )}
(對於k≥0{displaystyle kgeq 0},其中Γ(x,y){displaystyle Gamma (x,y)}是不完全Γ函數,⌊k⌋{displaystyle lfloor k floor }是高斯符號,Q是規則化Γ函數)期望值 λ{displaystyle lambda }中位數 ≈⌊λ+1/3−0.02/λ⌋{displaystyle approx lfloor lambda +1/3-0.02/lambda floor }眾數 ⌈λ⌉−1,⌊λ⌋{displaystyle lceil lambda ceil -1,lfloor lambda floor }變異數 λ{displaystyle lambda }偏度 λ−1/2{displaystyle lambda {-1/2}}峰度 λ−1{displaystyle lambda {-1}}熵λ[1−log(λ)]+e−λ∑k=0∞λklog(k!)k!{d...
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