/// <summary>
/// Returns NormalCdfMomentRatio(i,x) for i=n,n+1,n+2,...
/// </summary>
/// <param name="n">A starting index >= 0</param>
/// <param name="x">A real number</param>
/// <param name="useConFrac">If true, do not use the lookup table</param>
/// <returns></returns>
private static IEnumerator <double> NormalCdfMomentRatioSequence(int n, double x, bool useConFrac = false)
{
if (n < 0)
{
throw new ArgumentException("n < 0");
}
if (x > -1)
{
// Use the upward recurrence.
double rPrev = MMath.NormalCdfRatio(x);
if (n == 0)
{
yield return(rPrev);
}
double r = x * rPrev + 1;
if (n <= 1)
{
yield return(r);
}
for (int i = 1; ; i++)
{
double rNew = (x * r + rPrev) / (i + 1);
rPrev = r;
r = rNew;
if (n <= i + 1)
{
yield return(r);
}
}
}
else
{
// Use the downward recurrence.
// Each batch of tableSize items is generated in advance.
// If tableSize is larger than 50, the results will lose accuracy.
// If tableSize is too small, then the recurrence is used less often, requiring more computation.
int maxTableSize = 30;
// rtable[tableStart-i] = R_i
double[] rtable = new double[maxTableSize];
int tableStart = -1;
int tableSize = 2;
for (int i = n; ; i++)
{
if (i > tableStart)
{
// build the table
tableStart = i + tableSize - 1;
if (useConFrac)
{
rtable[0] = MMath.NormalCdfMomentRatioConFrac(tableStart, x);
rtable[1] = MMath.NormalCdfMomentRatioConFrac(tableStart - 1, x);
}
else
{
rtable[0] = MMath.NormalCdfMomentRatio(tableStart, x);
rtable[1] = MMath.NormalCdfMomentRatio(tableStart - 1, x);
}
for (int j = 2; j < tableSize; j++)
{
int nj = tableStart - j + 1;
if (rtable[j - 2] == 0 && rtable[j - 1] == 0)
{
rtable[j] = MMath.NormalCdfMomentRatio(nj - 1, x);
}
else
{
rtable[j] = (nj + 1) * rtable[j - 2] - x * rtable[j - 1];
}
}
// Increase tableSize up to the maximum.
tableSize = Math.Min(maxTableSize, 2 * tableSize);
}
yield return(rtable[tableStart - i]);
}
}
}
