/// <summary>
/// The Irwin-Hall distribution results from the sum on n independent standard uniform variables
/// </summary>
/// <param name="x">The value at which to evaluate the distribution.</param>
/// <param name="n">The number of standard uniform variables.</param>
public static double IrwinHallProbabilityDensityFunction(double x, int n)
{
if (x < 0 || x > n)
{
return(0.0);
}
double d = 0;
for (int i = 0; i <= n; i++)
{
d += Math.Pow(-1, i) * MMath.Combinations(n, i) * Math.Pow(x - i, n - 1) * Math.Sign(x - i);
}
d *= 0.5;
d /= MMath.Factorial(n - 1);
return(d);
}
/// <summary>
/// The PDF of the Poisson distribution.
/// The probability of n iid events occuring in an interval, if the expected number of event is lambda.
/// </summary>
/// <param name="lambda">Equals both the mean and variance of the distribution.</param>
/// <param name="n">The number of events.</param>
public static double PoissonProbabilityDensityFunction(double lambda, int n)
{
return(Math.Pow(lambda, n) * Math.Exp(-lambda) / MMath.Factorial(n));
}
