Difference between revisions of "Moment generating function"
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Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T}=\infty$. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a [[probability density function]]. The moment generating function of $f$ is defined to be | Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T}=\infty$. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a [[probability density function]]. The moment generating function of $f$ is defined to be | ||
$$M_f(z) = \displaystyle\int_0^{\infty} f(t) e_z(t,0) \Delta t.$$ | $$M_f(z) = \displaystyle\int_0^{\infty} f(t) e_z(t,0) \Delta t.$$ | ||
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| + | =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 17:26, 23 November 2014
Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T}=\infty$. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a probability density function. The moment generating function of $f$ is defined to be $$M_f(z) = \displaystyle\int_0^{\infty} f(t) e_z(t,0) \Delta t.$$
References
Probability theory on time scales and applications to finance and inequalities by Thomas Matthews
