public double Cdf(long k)
{var e = Math.Pow(Math.E, -_lambda);long i = 0;var sum = 0.0;while (i <= k){sum += e * Math.Pow(_lambda, i) / Factorial(i);i++;}return sum;
}

问题在于，随着k和_lambda（_lambda = λ）增加，分母都变得非常大，并且程序崩溃。这可以通过使用对数来解决。为简单起见，自然对数是用于：。计算中使用以下规则：

var log6ThTail = Math.Log(i * (1 + 4 * i * (1 + 2 * i)))/6;
var lnN = i * Math.Log(_lambda) - (i * Math.Log(i) - i + log6ThTail + logPiDivTwo);
n = Math.Pow(Math.E, lnN - _lambda);

这是代码：

using System;namespace PoissonEvaluator
{public class PoissonDistribution{private readonly double _lambda;public PoissonDistribution(double lambda = 1.0){_lambda = lambda;}public double Pmf(long k){if (k > 170 || double.IsInfinity(Math.Pow(_lambda, k))){var logLambda = k * Math.Log(_lambda) - _lambda - (k * Math.Log(k) - k +Math.Log(k * (1 + 4 * k * (1 + 2 * k))) / 6 + Math.Log(Math.PI) / 2);return Math.Pow(Math.E, logLambda);}return Math.Pow(Math.E, -_lambda) * Math.Pow(_lambda, k) / Factorial(k);}public double Cdf(long k){long i = 0;var sum = 0.0;var infinityIsFound = false;var eLambda = Math.Pow(Math.E, -_lambda);var logPiDivTwo = Math.Log(Math.PI) / 2;while (i <= k){double n;if (infinityIsFound){var log6ThTail = Math.Log(i * (1 + 4 * i * (1 + 2 * i))) / 6;var lnN = i * Math.Log(_lambda) - (i * Math.Log(i) - i +log6ThTail + logPiDivTwo);n = Math.Pow(Math.E, lnN - _lambda);}else{if (i > 170 || double.IsInfinity(Math.Pow(_lambda, i))){infinityIsFound = true;var log6ThTail = Math.Log(i * (1 + 4 * i * (1 + 2 * i))) / 6;var lnN = i * Math.Log(_lambda) - (i * Math.Log(i) - i +log6ThTail + logPiDivTwo);n = Math.Pow(Math.E, lnN - _lambda);}else{n = eLambda * Math.Pow(_lambda, i) / Factorial(i);}}sum += n;i++;}return (sum > 1) ? 1.0 : sum;}public double Factorial(long k){long count = k;double factorial = 1;while (count >= 1){factorial = factorial * count;count--;}return factorial;}}