CauchyDistribution.scala

def cauchyCDF(gamma: Double = 1.0, x0: Double = 0.0) = (x: Double) =>
  1.0/math.Pi * math.atan((x-x0) / gamma) + 0.5

val f = cauchyCDF()

(-6.0 to 6.0 by 0.1).map(f).plot()

// y - 0.5 = 1.0/math.Pi * math.atan((x-x0) / gamma)
// 
// (y - 0.5) * math.Pi = math.atan((x-x0) / gamma)
// 
// math.tan((y - 0.5) * math.Pi) = (x-x0) / gamma
// 
// math.tan((y - 0.5) * math.Pi) * gamma = x - x0
// 
// math.tan((y - 0.5) * math.Pi) * gamma + x0 = x

def genCauchy(gamma: Double = 1.0, x0: Double = 0.0) = {
  val y = math.random()
  math.tan((y - 0.5) * math.Pi) * gamma + x0
}

val xs = Vector.fill(10000)(genCauchy())

val histo = (-6.0 to 6.0 by 0.1).map { lo => xs.count(x => x >= lo && x < lo + 0.1) }

histo.plot()

val xs2 = Vector.fill(10000)(genCauchy(gamma = 2))

val histo2 = (-6.0 to 6.0 by 0.1).map { lo => xs2.count(x => x >= lo && x < lo + 0.1) }

histo2.plot()