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Arcsine distribution

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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Characteristic function

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Overview

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Related distributions

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CDF
F ( x ) = 2 π arcsin ⁡ ( x ) {\displaystyle F(x)={\frac {2}{\pi }}\arcsin \left({\sqrt {x}}\right)}
CF
e i t 2 J 0 ( t 2 ) {\displaystyle e^{i{\frac {t}{2}}}J_{0}({\frac {t}{2}})}
Entropy
log ⁡ π 4 {\displaystyle \log {\tfrac {\pi }{4}}}
Excess kurtosis
− 3 2 {\displaystyle -{\tfrac {3}{2}}}
Mean
1 2 {\displaystyle {\frac {1}{2}}}
Median
1 2 {\displaystyle {\frac {1}{2}}}

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Overview

Characteristic function

Related distributions

  • I.i.d Independent and identically distributed random variables
  • Uniform Uniform distribution (continuous)

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Arcsine distribution

Nodes21
Edges20
Triples38
Avg. degree1.9
Density0.095238
Components1

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Arcsine distribution

Top relations

related to Related distributions · 6
Arcsine distribution → Arcsine, Beta, Cauchy, If, U-V, X-a
related to Further reading · 5
Arcsine distribution → Arcsine, EMS Press, Encyclopedia, Mathematics, Rogozin
is a · 4
Arcsine distribution → probability distribution whose cumulative distribution function involves the arcsine and the square root, special case of the beta distribution with α, special case of the Pearson type I distribution.The arcsine distribution appears in the Lévy arcsine law, zero order Bessel function of the first kind
related to Properties · 4
Arcsine distribution → Arcsine, If, The, Uniform
related to Characteristic function · 3
Arcsine distribution → Bessel, For, The
related to Shape factor · 2
Arcsine distribution → Beta, The
CDF · 1
Arcsine distribution → F ( x ) = 2 π arcsin ⁡ ( x ) {\displaystyle F(x)={\frac {2}{\pi }}\arcsin \left({\sqrt {x}}\right)}
CF · 1
Arcsine distribution → e i t 2 J 0 ( t 2 ) {\displaystyle e^{i{\frac {t}{2}}}J_{0}({\frac {t}{2}})}
Entropy · 1
Arcsine distribution → log ⁡ π 4 {\displaystyle \log {\tfrac {\pi }{4}}}
Excess kurtosis · 1
Arcsine distribution → − 3 2 {\displaystyle -{\tfrac {3}{2}}}

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Important terminology

distribution arcsine probability displaystyle function density lead tfrac random rm special case beta player number times standard frac sin -1

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Arcsine distributionCDFF ( x ) = 2 π arcsin ⁡ ( x ) {\displaystyle F(x)={\frac {2}{\pi }}\arcsin \left({\sqrt {x}}\right)}1.00infobox
Arcsine distributionCFe i t 2 J 0 ( t 2 ) {\displaystyle e^{i{\frac {t}{2}}}J_{0}({\frac {t}{2}})}1.00infobox
Arcsine distributionEntropylog ⁡ π 4 {\displaystyle \log {\tfrac {\pi }{4}}}1.00infobox
Arcsine distributionExcess kurtosis− 3 2 {\displaystyle -{\tfrac {3}{2}}}1.00infobox
Arcsine distributionMean1 2 {\displaystyle {\frac {1}{2}}}1.00infobox
Arcsine distributionMedian1 2 {\displaystyle {\frac {1}{2}}}1.00infobox
Arcsine distributionMGF1 + ∑ 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!}}}1.00infobox
Arcsine distributionModex ∈ { 0 , 1 } {\displaystyle x\in \{0,1\}}1.00infobox
Arcsine distributionParametersnone1.00infobox
Arcsine distributionPDFf ( x ) = 1 π x ( 1 − x ) {\displaystyle f(x)={\frac {1}{\pi {\sqrt {x(1-x)}}}}}1.00infobox
Arcsine distributionQuantileF − 1 ( x ) = sin ⁡ ( π x 2 ) 2 {\displaystyle F^{-1}(x)=\sin \left({\frac {\pi x}{2}}\right)^{2}}1.00infobox
Arcsine distributionSkewness0 {\displaystyle 0}1.00infobox
Arcsine distributionSupportx ∈ ( 0 , 1 ) {\displaystyle x\in (0,1)}1.00infobox
Arcsine distributionVariance1 8 {\displaystyle {\tfrac {1}{8}}}1.00infobox
Arcsine distributionis aprobability distribution whose cumulative distribution function involves the arcsine and the square root0.90text
Arcsine distributionis aspecial case of the beta distribution with α0.90text
Arcsine distributionis aspecial case of the Pearson type I distribution.The arcsine distribution appears in the Lévy arcsine law0.90text
Arcsine distributionis azero order Bessel function of the first kind0.90text

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