Function distributionCDF

src/compute-engine/library/distributions.ts:338–407

(
  ce: ComputeEngine,
  dist: Expression,
  x: Expression
)

      const z = sub(x, mu);
      const num = fn('Exp', [
        neg(
          div(
            pow(z, ce.number(2)),
            mul([ce.number(2), pow(sigma, ce.number(2))])
          )
        ),
      ]);
      const den = mul([sigma, fn('Sqrt', [mul([ce.number(2), ce.Pi])])]);
      return div(num, den);
    }

    case 'BinomialDistribution': {
      const [n, p] = distOps(dist);
      // Discrete: density at a numeric non-integer point is 0.
      if (xv !== undefined && !Number.isInteger(xv)) return ce.Zero;
      const k = x;
      return mul([
        fn('Binomial', [n, k]),
        pow(p, k),
        pow(sub(ce.One, p), sub(n, k)),
      ]);
    }

    case 'PoissonDistribution': {
      const [lambda] = distOps(dist);
      if (xv !== undefined && !Number.isInteger(xv)) return ce.Zero;
      const k = x;
      return div(
        mul([pow(lambda, k), fn('Exp', [neg(lambda)])]),
        fn('Factorial', [k])
      );
    }

    case 'UniformDistribution': {
      const [a, b] = distOps(dist);
      const av = litVal(a);
      const bv = litVal(b);
      // Numeric point outside the support has zero density.
      if (
        xv !== undefined &&
        av !== undefined &&
        bv !== undefined &&
        (xv < av || xv > bv)
      )
        return ce.Zero;
      return div(ce.One, sub(b, a));
    }

    case 'ExponentialDistribution': {
      const [lambda] = distOps(dist);
      if (xv !== undefined && xv < 0) return ce.Zero;
      return mul([lambda, fn('Exp', [neg(mul([lambda, x]))])]);
    }
  }
  return undefined;
}

function distributionCDF(