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gptkbp:instanceOf
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gptkb:Probability_distribution
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gptkbp:alsoKnownAs
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Arcsine distribution
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gptkbp:category
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univariate distribution
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gptkbp:cumulativeDistributionFunction
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F(x) = (2/π) arcsin(√x) for x in [0,1]
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gptkbp:domain
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real numbers between 0 and 1
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gptkbp:entropy
|
ln(π/4)
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gptkbp:firstMoment
|
0.5
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gptkbp:fourthMoment
|
0.1875
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gptkbp:hasFatTails
|
true
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gptkbp:hasSpecialCase
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Beta(1/2,1/2) distribution
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gptkbp:kurtosis
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-1.5
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gptkbp:meaning
|
0.5
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gptkbp:medium
|
0.5
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gptkbp:mode
|
0
1
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gptkbp:namedAfter
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arcsine function
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gptkbp:parameter
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none (standard form)
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gptkbp:probabilityDensityFunction
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f(x) = 1 / (π√(x(1-x))) for x in (0,1)
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gptkbp:relatedTo
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gptkb:Beta_distribution
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gptkbp:secondMoment
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0.375
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gptkbp:skewness
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0
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gptkbp:supports
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[0,1]
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gptkbp:symmetry
|
true
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gptkbp:thirdMoment
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0.25
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gptkbp:type
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continuous distribution
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gptkbp:usedIn
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gptkb:probability_theory
Brownian motion
random walk theory
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gptkbp:variant
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1/8
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gptkbp:bfsParent
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gptkb:Arcsine_distribution_(when_alpha=beta=0.5)
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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Arcsin distribution
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