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]]
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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.$$
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=Properties=
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[[Expected value of exponential distribution]]<br />
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[[Variance of exponential distribution]]
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=References=
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[http://scholarsmine.mst.edu/doctoral_dissertations/2241/]
  
 
{{:Probability distributions footer}}
 
{{:Probability distributions footer}}
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[[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

[1]

Probability distributions

Uniform distributionExponential distributionGamma distribution