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Format:

Beta(Min, Max, α, β

Probability density function:

f(x)=\frac{z^{\alpha-1} (1-z)^{\beta-1}}{(max-min)^2 \int\limits_0^1 t^{\alpha-1 }(1-t)^ {\beta-1} dt}
z=\frac{x-Min} {Max-Min}

Cumulative distribution function:

No closed form

Parameter restrictions:

α > 0, β > 0

Domain: 

Min ≤ x ≤ Max 

Mean:

α * (Max - Min) / (α + β) + Min

Mode: 

\frac{\alpha_1-1}{\alpha_1+\alpha_2-2}

if α1 > 1, α2 > 1

0 , 1

 if α1 < 1, α2 < 1

0

 if α1 < 1, α2 ≥ 1 or if α1 = 1, α2 > 1

1

if α1 ≥ 1, α2 < 1 or if α1 > 1, α2 = 1

 does not uniquely exist if α1 = 1, α2 = 1

Variance:

(max-min)^2 \frac{\alpha\beta}{(\alpha+\beta)^2 (\alpha+\beta+1)}




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