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