Distribución Gamma
Gamma(α, λ): \(f(y)=\frac{\lambda^\alpha}{\Gamma(\alpha)} y^{\alpha-1} e^{-\lambda y}\), \(y>0\)
\(\mathbb{E}[Y]=\frac{\alpha}{\lambda}=\alpha\beta\), \(\operatorname{var}(Y)=\frac{\alpha}{\lambda^2}=\alpha\beta^2\)
Casos especiales: α=1 → Exponencial; α=n/2, β=2 → χ²ₙ
\(\mathbb{E}[Y]=\frac{\alpha}{\lambda}=\alpha\beta\), \(\operatorname{var}(Y)=\frac{\alpha}{\lambda^2}=\alpha\beta^2\)
Casos especiales: α=1 → Exponencial; α=n/2, β=2 → χ²ₙ
Explorador de Gamma
2.0
1.0
Función Gamma: \(\Gamma(x)=\int_0^\infty u^{x-1}e^{-u}du\)
Propiedades: \(\Gamma(x+1)=x\Gamma(x)\), \(\Gamma(1)=1\), \(\Gamma(1/2)=\sqrt{\pi}\), \(\Gamma(n+1)=n!\)
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