private Moments GetMoments([NotNull] Sample sample, Probability probability)
{
Assertion.NotNull(nameof(sample), sample);
double n = sample.WeightedCount;
double a = (n + 1) * probability, b = (n + 1) * (1 - probability);
var distribution = new BetaDistribution(a, b);
double targetPercent = 1.0 - TrimPercent;
bool symmetricMode = Math.Abs(probability - 0.5) < 1e-9;
double c1 = 0;
double c2 = 0;
void Process(int j, double w)
{
c1 += w * sample.SortedValues[j];
c2 += w * sample.SortedValues[j].Sqr();
}
double GetElementProbability(int j) => sample.IsWeighted
? sample.SortedWeights[j] / sample.TotalWeight
: 1.0 / sample.Count;
// Preparation
double probabilityLeft = 0, probabilityRight = 0;
int indexLeft;
for (indexLeft = 0; indexLeft < sample.Count; indexLeft++)
{
double elementProbability = GetElementProbability(indexLeft);
probabilityLeft = probabilityRight;
probabilityRight = probabilityLeft + elementProbability;
if (probabilityRight >= probability || indexLeft == sample.Count - 1)
{
break;
}
}
int indexRight = indexLeft;
double betaCdfLeft = distribution.Cdf(probabilityLeft);
double betaCdfRight = distribution.Cdf(probabilityRight);
Process(indexLeft, betaCdfRight - betaCdfLeft);
double betaPdfLeft = distribution.Pdf(probabilityLeft);
double betaPdfRight = distribution.Pdf(probabilityRight);
while ((betaCdfRight - betaCdfLeft < targetPercent ||
symmetricMode && (indexLeft != sample.Count - 1 - indexRight)) &&
(indexLeft > 0 || indexRight < sample.Count - 1))
{
if (indexLeft > 0 && (betaPdfLeft > betaPdfRight || indexRight == sample.Count - 1))
{
// Expand to the left
int indexNext = indexLeft - 1;
double probabilityNext = probabilityLeft - GetElementProbability(indexNext);
double betaCdfNext = distribution.Cdf(probabilityNext);
double betaPdfNext = distribution.Pdf(probabilityNext);
Process(indexNext, betaCdfLeft - betaCdfNext);
indexLeft = indexNext;
probabilityLeft = probabilityNext;
betaCdfLeft = betaCdfNext;
betaPdfLeft = betaPdfNext;
}
else
{
// Expand to the right
int indexNext = indexRight + 1;
double probabilityNext = probabilityRight + GetElementProbability(indexNext);
double betaCdfNext = distribution.Cdf(probabilityNext);
double betaPdfNext = distribution.Pdf(probabilityNext);
Process(indexNext, betaCdfNext - betaCdfRight);
indexRight = indexNext;
probabilityRight = probabilityNext;
betaCdfRight = betaCdfNext;
betaPdfRight = betaPdfNext;
}
}
if (IsWinsorized)
{
// Processing winsorized elements
Process(indexLeft, betaCdfLeft);
Process(indexRight, 1 - betaCdfRight);
}
else
{
double scaleFactor = 1 / (betaCdfRight - betaCdfLeft);
c1 *= scaleFactor;
c2 *= scaleFactor;
}
return(new Moments(c1, c2, indexLeft, indexRight));
}