Difference between revisions of "Probability density function"
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Let $\mathbb{T}$ be a [[time scale]] with $0 \in \mathbb{T}$ and $\sup \mathbb{T} = \infty$. A function $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is called a probability density function if $f(t) \geq 0$ for all $t \in \mathbb{T}$ and | Let $\mathbb{T}$ be a [[time scale]] with $0 \in \mathbb{T}$ and $\sup \mathbb{T} = \infty$. A function $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is called a probability density function if $f(t) \geq 0$ for all $t \in \mathbb{T}$ and | ||
$$\displaystyle\int_0^{\infty} f(t) \Delta t = 1.$$ | $$\displaystyle\int_0^{\infty} f(t) \Delta t = 1.$$ | ||
| + | |||
| + | *[[Uniform distribution]] | ||
| + | *[[Exponential distribution]] | ||
| + | *[[Gamma distribution]] | ||
| + | |||
| + | =References= | ||
| + | [https://mospace.umsystem.edu/xmlui/bitstream/handle/10355/29595/Matthews_2011.pdf?sequence=1 Probability theory on time scales and applications to finance and inequalities by Thomas Matthews] | ||
Latest revision as of 21:44, 14 April 2015
Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T} = \infty$. A function $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is called a probability density function if $f(t) \geq 0$ for all $t \in \mathbb{T}$ and $$\displaystyle\int_0^{\infty} f(t) \Delta t = 1.$$
References
Probability theory on time scales and applications to finance and inequalities by Thomas Matthews
