Function binomialQuantile

src/compute-engine/numerics/distributions.ts:59–72

(
  n: number,
  p: number,
  prob: number,
  deadline?: number
)

/** Quantile of Binomial(n, p) at probability `prob` (an integer in [0, n]). */
export function binomialQuantile(
  n: number,
  p: number,
  prob: number,
  deadline?: number
): number {
  const mean = n * p;
  const stddev = Math.sqrt(n * p * (1 - p));
  // CDF(k) = P(X ≤ k) = I_{1−p}(n−k, k+1); the kernel is undefined at a=0,
  // so the k ≥ n endpoint (CDF = 1) is handled explicitly.
  const cdf = (k: number): number =>
    k >= n ? 1 : k < 0 ? 0 : betaRegularized(1 - p, n - k, k + 1);
  return discreteQuantile(cdf, prob, mean, stddev, 0, n, deadline);
}

/** Quantile of Poisson(λ) at probability `prob` (a non-negative integer). */
export function poissonQuantile(