Difference between revisions of "Exponential distribution"
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| − | Let $\mathbb{T}$ be a time scale. Let $\lambda > 0$ and $\ominus \lambda$ be positively regressive and let $t \in \mathbb{T}$. The exponential distribution is given by the [[probability density function]] | + | __NOTOC__ |
| + | Let $\mathbb{T}$ be a time scale. Let $\lambda > 0$ and $\ominus \lambda$ be [[positively mu regressive | positively $\mu$-regressive]] constant functions and let $t \in \mathbb{T}$. The exponential distribution is given by the [[probability density function]] | ||
$$f(t) = \left\{ \begin{array}{ll} | $$f(t) = \left\{ \begin{array}{ll} | ||
-(\ominus \lambda)(t) e_{\ominus \lambda}(t,0) &; t \geq 0 \\ | -(\ominus \lambda)(t) e_{\ominus \lambda}(t,0) &; t \geq 0 \\ | ||
0 &; t<0. | 0 &; t<0. | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Expected value of exponential distribution]]<br /> | ||
| + | [[Variance of exponential distribution]] | ||
| + | |||
| + | =References= | ||
| + | [http://scholarsmine.mst.edu/doctoral_dissertations/2241/] | ||
| + | |||
| + | {{:Probability distributions footer}} | ||
| + | |||
| + | [[Category:Definition]] | ||
Latest revision as of 14:07, 28 January 2023
Let $\mathbb{T}$ be a time scale. Let $\lambda > 0$ and $\ominus \lambda$ be positively $\mu$-regressive constant functions and let $t \in \mathbb{T}$. The exponential distribution is given by the probability density function $$f(t) = \left\{ \begin{array}{ll} -(\ominus \lambda)(t) e_{\ominus \lambda}(t,0) &; t \geq 0 \\ 0 &; t<0. \end{array} \right.$$
Properties
Expected value of exponential distribution
Variance of exponential distribution
References
Probability distributions | ||
| Uniform distribution | Exponential distribution | Gamma distribution |
