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  1. ```
  2. override def cumulativeProbability(x: Double): Double = {
  3.     // An approximation to the true CDF since numerical integration diverges.
  4.     // Source and notation: https://www.sciencedirect.com/science/article/pii/S209012321000069X.
  5.     val standardizedX = (x - location) / scale
  6.  
  7.     if (standardizedX < -3) 0.0
  8.     else if (-3 <= standardizedX && standardizedX < -1) H1(standardizedX)
  9.     else if (-1 <= standardizedX && standardizedX < 1) H2(standardizedX)
  10.     else if (1 <= standardizedX && standardizedX < 3) H3(standardizedX)
  11.     else 1.0
  12.   }
  13.  
  14. private def H1(x: Double): Double = {
  15.     val first = (3 * SHAPESQ + 9) * gI(-3 / shape, x)
  16.     val second = shape * (3 + 2 / 3 * SHAPESQ) * math.exp(-9 / (2 * SHAPESQ))
  17.     val third = -shape * (9 + 2 / 3 * SHAPESQ + 3 * shape * x + SHAPESQ * x * x / 3) * math.exp(-x * x / 2)
  18.     (first + second + third) / (8 * SQRT2PI)
  19.   }
  20.  
  21.   private def H2(x: Double): Double = {
  22.     val first = (3 * SHAPESQ + 9) * gI(-3 / shape, -1 / shape)
  23.     val second = 8 * gI(-1 / shape, x)
  24.     val third = shape * (3 + 2 / 3 * SHAPESQ) * math.exp(-9 / (2 * SHAPESQ))
  25.     val fourth = -shape * (1 + 2 * SHAPESQ) * math.exp(-1 / (2 * SHAPESQ))
  26.     val fifth = 2 / 3 * shape * (-9 + 2 * SHAPESQ + SHAPESQ * x * x) * math.exp(-x * x / 2)
  27.     (first + second + third + fourth + fifth) / (8 * SQRT2PI)
  28.   }
  29.  
  30.   private def H3(x: Double): Double = {
  31.     val first = (3 * SHAPESQ + 9) * gI(-3 / shape, -1 / shape)
  32.     val second = 8 * gI(-1 / shape, 1 / shape)
  33.     val third = (7 - 3 * SHAPESQ) * gI(1 / shape, x)
  34.     val fourth = shape * (3 + 2 / 3 * SHAPESQ) * math.exp(-9 / (2 * SHAPESQ))
  35.     val fifth = -shape / 3 * (27 - 9 * shape * x + SHAPESQ * x * x + 2 * SHAPESQ) * math.exp(-x * x / 2)
  36.     (first + second + third + fourth + fifth) / (8 * SQRT2PI)
  37.   }
  38.  
  39.   // Integrate exp(-x^2 / 2) from a to b.
  40.   private def gI(a: Double, b: Double): Double = SQRT2PI / 2 * Erf.erf(a / SQRT2PI, b / SQRT2PI)
  41. ```
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