Difference between revisions of "Arcsin cdf"
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(Created page with "The arcsin cumulative distribution function $F \colon [0,1] \rightarrow \mathbb{R}$ is given by $$F(x) = \dfrac{2}{\pi} \arcsin\left(\sqrt{x} \right),$$ where $\pi$ denot...") |
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The arcsin [[cumulative distribution function]] $F \colon [0,1] \rightarrow \mathbb{R}$ is given by | The arcsin [[cumulative distribution function]] $F \colon [0,1] \rightarrow \mathbb{R}$ is given by | ||
| − | $$F(x) = \dfrac{2}{\pi} \arcsin\left(\sqrt{x} \right),$$ | + | $$F(x) = \left\{ \begin{array}{ll} |
| + | 0, & \quad x<0 \\ | ||
| + | \dfrac{2}{\pi} \arcsin\left(\sqrt{x} \right), & \quad 0 \leq x \leq 1 \\ | ||
| + | 1, & \quad x>1, | ||
| + | \end{array} \right.$$ | ||
where $\pi$ denotes [[pi]] and $\arcsin$ denotes [[arcsin]]. | where $\pi$ denotes [[pi]] and $\arcsin$ denotes [[arcsin]]. | ||
Latest revision as of 03:35, 12 March 2018
The arcsin cumulative distribution function $F \colon [0,1] \rightarrow \mathbb{R}$ is given by $$F(x) = \left\{ \begin{array}{ll} 0, & \quad x<0 \\ \dfrac{2}{\pi} \arcsin\left(\sqrt{x} \right), & \quad 0 \leq x \leq 1 \\ 1, & \quad x>1, \end{array} \right.$$ where $\pi$ denotes pi and $\arcsin$ denotes arcsin.
