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In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square root:
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Arcsine distribution | CDF | F ( x ) = 2 π arcsin ( x ) {\displaystyle F(x)={\frac {2}{\pi }}\arcsin \left({\sqrt {x}}\right)} | 1.00 | infobox |
| Arcsine distribution | CF | e i t 2 J 0 ( t 2 ) {\displaystyle e^{i{\frac {t}{2}}}J_{0}({\frac {t}{2}})} | 1.00 | infobox |
| Arcsine distribution | Entropy | log π 4 {\displaystyle \log {\tfrac {\pi }{4}}} | 1.00 | infobox |
| Arcsine distribution | Excess kurtosis | − 3 2 {\displaystyle -{\tfrac {3}{2}}} | 1.00 | infobox |
| Arcsine distribution | Mean | 1 2 {\displaystyle {\frac {1}{2}}} | 1.00 | infobox |
| Arcsine distribution | Median | 1 2 {\displaystyle {\frac {1}{2}}} | 1.00 | infobox |
| Arcsine distribution | MGF | 1 + ∑ k = 1 ∞ ( ∏ r = 0 k − 1 2 r + 1 2 r + 2 ) t k k ! {\displaystyle 1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {2r+1}{2r+2}}\right){\frac {t^{k}}{k!}}} | 1.00 | infobox |
| Arcsine distribution | Mode | x ∈ { 0 , 1 } {\displaystyle x\in \{0,1\}} | 1.00 | infobox |
| Arcsine distribution | Parameters | none | 1.00 | infobox |
| Arcsine distribution | f ( x ) = 1 π x ( 1 − x ) {\displaystyle f(x)={\frac {1}{\pi {\sqrt {x(1-x)}}}}} | 1.00 | infobox | |
| Arcsine distribution | Quantile | F − 1 ( x ) = sin ( π x 2 ) 2 {\displaystyle F^{-1}(x)=\sin \left({\frac {\pi x}{2}}\right)^{2}} | 1.00 | infobox |
| Arcsine distribution | Skewness | 0 {\displaystyle 0} | 1.00 | infobox |
| Arcsine distribution | Support | x ∈ ( 0 , 1 ) {\displaystyle x\in (0,1)} | 1.00 | infobox |
| Arcsine distribution | Variance | 1 8 {\displaystyle {\tfrac {1}{8}}} | 1.00 | infobox |
| Arcsine distribution | is a | probability distribution whose cumulative distribution function involves the arcsine and the square root | 0.90 | text |
| Arcsine distribution | is a | special case of the beta distribution with α | 0.90 | text |
| Arcsine distribution | is a | special case of the Pearson type I distribution.The arcsine distribution appears in the Lévy arcsine law | 0.90 | text |
| Arcsine distribution | is a | zero order Bessel function of the first kind | 0.90 | text |
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