Difference between revisions of "Uniform distribution"
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Let $\mathbb{T}$ be a [[time scale]]. Let $a,b \in \mathbb{T}$. The uniform distribution on the interval $[a,b] \cap \mathbb{T}$ is given by the formula | Let $\mathbb{T}$ be a [[time scale]]. Let $a,b \in \mathbb{T}$. The uniform distribution on the interval $[a,b] \cap \mathbb{T}$ is given by the formula | ||
$$U_{[a,b]}(t) = \left\{ \begin{array}{ll} | $$U_{[a,b]}(t) = \left\{ \begin{array}{ll} | ||
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0 &; \mathrm{otherwise} | 0 &; \mathrm{otherwise} | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Expected value of uniform distribution]]<br /> | ||
| + | [[Variance of uniform distribution]]<br /> | ||
| + | |||
| + | =References= | ||
| + | [http://scholarsmine.mst.edu/doctoral_dissertations/2241/] | ||
| + | |||
| + | {{:Probability distributions footer}} | ||
Latest revision as of 01:22, 30 September 2018
Let $\mathbb{T}$ be a time scale. Let $a,b \in \mathbb{T}$. The uniform distribution on the interval $[a,b] \cap \mathbb{T}$ is given by the formula $$U_{[a,b]}(t) = \left\{ \begin{array}{ll} \dfrac{1}{\sigma(b)-a} &; a \leq t \leq b \\ 0 &; \mathrm{otherwise} \end{array} \right.$$
Properties
Expected value of uniform distribution
Variance of uniform distribution
References
Probability distributions | ||
| Uniform distribution | Exponential distribution | Gamma distribution |
