Wigner semicircle distribution (ArcSin CDF)
WignerSemicircleDistribution[r]
WignerSemicircleDistribution[a, r]
PDF[WignerSemicircleDistribution[r], x]
→ Piecewise[{{(2*Sqrt[1 - x^2/r^2])/(Pi*r), -r < x < r}}, 0]CDF[WignerSemicircleDistribution[r], x]
→ Piecewise[{{1/2 + (x*Sqrt[1 - x^2/r^2])/(Pi*r) + ArcSin[x/r]/Pi, -r < x < r}, {1, x >= r}}, 0]PDF[WignerSemicircleDistribution[a, r], x]
→ Piecewise[{{(2*Sqrt[1 - (-a + x)^2/r^2])/(Pi*r), a - r < x < a + r}}, 0]