Difference between revisions of "Gamma distribution"

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Let $\mathbb{T}$ be a time scale. Let $\lambda \in \mathbb{R}$ with $\lambda > 0$ and define $\Lambda_0(t,t_0)=0, \Lambda_1(t,t_0)=1$. The gamma distribution is the [[probability density function]] defined recursively for $k \geq 2$ by the formula
 
Let $\mathbb{T}$ be a time scale. Let $\lambda \in \mathbb{R}$ with $\lambda > 0$ and define $\Lambda_0(t,t_0)=0, \Lambda_1(t,t_0)=1$. The gamma distribution is the [[probability density function]] defined recursively for $k \geq 2$ by the formula
 
$$\Lambda_{k+1}(t,t_0) = -\displaystyle\int_{t_0}^t (\ominus \lambda)(\tau) \Lambda_k(\sigma(\tau),t_0) \Delta \tau.$$
 
$$\Lambda_{k+1}(t,t_0) = -\displaystyle\int_{t_0}^t (\ominus \lambda)(\tau) \Lambda_k(\sigma(\tau),t_0) \Delta \tau.$$
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Revision as of 18:51, 21 March 2015

Let $\mathbb{T}$ be a time scale. Let $\lambda \in \mathbb{R}$ with $\lambda > 0$ and define $\Lambda_0(t,t_0)=0, \Lambda_1(t,t_0)=1$. The gamma distribution is the probability density function defined recursively for $k \geq 2$ by the formula $$\Lambda_{k+1}(t,t_0) = -\displaystyle\int_{t_0}^t (\ominus \lambda)(\tau) \Lambda_k(\sigma(\tau),t_0) \Delta \tau.$$

Probability distributions

Uniform distributionExponential distributionGamma distribution