Continuous binomial distribution

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Definition

Irwin–Hall distribution Natural exponential family

2 related topics

Related distributions

Bates distribution Continuous uniform distribution

2 related topics

Properties

Beta distribution

1 related topics

Overview

Probability theory Statistics Exponential dispersion family Generalized linear models Beta regression

6 related topics

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Mean: B ′ ( θ ) = { e θ e θ − 1 − 1 θ , θ ≠ 0 , 1 2 , θ = 0 , {\displaystyle B'(\theta )={\begin{cases}{\frac {e^{\theta }}{e^{\theta }-1}}-{\frac {1}{\theta }},&\theta \neq 0,\\{\fra…
Parameters: θ ∈ R {\displaystyle \theta \in \mathbb {R} } (natural parameter) λ ∈ { 1 , 2 , 3 , … } {\displaystyle \lambda \in \{1,2,3,\dots \}} (inverse dispersion)
PDF: f ( x ; θ , λ ) = h ( x ; λ ) exp ( λ θ x − λ B ( θ ) ) , 0 ≤ x ≤ 1 , {\displaystyle f(x;\theta ,\lambda )=h(x;\lambda )\exp \!{\big (}\lambda \theta x-\lambda B(\theta ){\big )…
Support: x ∈ [ 0 , 1 ] {\displaystyle x\in [0,1]} if λ = 1 {\displaystyle \lambda =1} , x ∈ ( 0 , 1 ) {\displaystyle x\in (0,1)} if λ ≥ 2 {\displaystyle \lambda \geq 2}
Variance: 1 λ B ″ ( θ ) = { 1 λ ( 1 θ 2 − e θ ( e θ − 1 ) 2 ) , θ ≠ 0 , 1 12 λ , θ = 0. {\displaystyle {\frac {1}{\lambda }}B''(\theta )={\begin{cases}{\frac {1}{\lambda }}\left({\frac {1…

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Overview

Probability theory
Statistics
Exponential dispersion family Exponential dispersion model
Generalized linear models Generalized linear model
Beta regression
Continuous Bernoulli distribution

Definition

Related distributions

Properties

Beta distribution

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Map overview Semantic statistics

Nodes16

Edges15

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Avg. degree1.88

Density0.125

Components1

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Continuous binomial distribution

Top relations

Mean · 1

Continuous binomial distribution → B ′ ( θ ) = { e θ e θ − 1 − 1 θ , θ ≠ 0 , 1 2 , θ = 0 , {\displaystyle B'(\theta )={\begin{cases}{\frac {e^{\theta }}{e^{\theta }-1}}-{\frac {1}{\theta }},&\theta \neq 0,\\{\fra…

Parameters · 1

Continuous binomial distribution → θ ∈ R {\displaystyle \theta \in \mathbb {R} } (natural parameter) λ ∈ { 1 , 2 , 3 , … } {\displaystyle \lambda \in \{1,2,3,\dots \}} (inverse dispersion)

PDF · 1

Continuous binomial distribution → f ( x ; θ , λ ) = h ( x ; λ ) exp ( λ θ x − λ B ( θ ) ) , 0 ≤ x ≤ 1 , {\displaystyle f(x;\theta ,\lambda )=h(x;\lambda )\exp \!{\big (}\lambda \theta x-\lambda B(\theta ){\big )…

Support · 1

Continuous binomial distribution → x ∈ [ 0 , 1 ] {\displaystyle x\in [0,1]} if λ = 1 {\displaystyle \lambda =1} , x ∈ ( 0 , 1 ) {\displaystyle x\in (0,1)} if λ ≥ 2 {\displaystyle \lambda \geq 2}

Variance · 1

Continuous binomial distribution → 1 λ B ″ ( θ ) = { 1 λ ( 1 θ 2 − e θ ( e θ − 1 ) 2 ) , θ ≠ 0 , 1 12 λ , θ = 0. {\displaystyle {\frac {1}{\lambda }}B''(\theta )={\begin{cases}{\frac {1}{\lambda }}\left({\frac {1…

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Important terminology

displaystyle lambda distribution theta continuous frac -1 mean cobin neq natural parameter dispersion random dots begin cases end max variance

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Continuous binomial distribution	Mean	B ′ ( θ ) = { e θ e θ − 1 − 1 θ , θ ≠ 0 , 1 2 , θ = 0 , {\displaystyle B'(\theta )={\begin{cases}{\frac {e^{\theta }}{e^{\theta }-1}}-{\frac {1}{\theta }},&\theta \neq 0,\\{\fra…	1.00	infobox
Continuous binomial distribution	Parameters	θ ∈ R {\displaystyle \theta \in \mathbb {R} } (natural parameter) λ ∈ { 1 , 2 , 3 , … } {\displaystyle \lambda \in \{1,2,3,\dots \}} (inverse dispersion)	1.00	infobox
Continuous binomial distribution	PDF	f ( x ; θ , λ ) = h ( x ; λ ) exp ( λ θ x − λ B ( θ ) ) , 0 ≤ x ≤ 1 , {\displaystyle f(x;\theta ,\lambda )=h(x;\lambda )\exp \!{\big (}\lambda \theta x-\lambda B(\theta ){\big )…	1.00	infobox
Continuous binomial distribution	Support	x ∈ [ 0 , 1 ] {\displaystyle x\in [0,1]} if λ = 1 {\displaystyle \lambda =1} , x ∈ ( 0 , 1 ) {\displaystyle x\in (0,1)} if λ ≥ 2 {\displaystyle \lambda \geq 2}	1.00	infobox
Continuous binomial distribution	Variance	1 λ B ″ ( θ ) = { 1 λ ( 1 θ 2 − e θ ( e θ − 1 ) 2 ) , θ ≠ 0 , 1 12 λ , θ = 0. {\displaystyle {\frac {1}{\lambda }}B''(\theta )={\begin{cases}{\frac {1}{\lambda }}\left({\frac {1…	1.00	infobox

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