// see introselect http://en.wikipedia.org/wiki/Selection_algorithm#Introselect and impl of the sort in arraysorthelper
// replacing given parts of a sample at the high and low end with the most extreme remaining values
public OfflineUnivariateStat Winsorize(double percent = 0.25)
{
OfflineUnivariateStat newStat = new OfflineUnivariateStat();
int sizeToCut = (int)(data.Count * percent);
for (int i = 0; i < sizeToCut; i++)
{
newStat.Add(data[sizeToCut]);
}
for (int i = sizeToCut; i < data.Count - sizeToCut; i++)
{
newStat.Add(data[i]);
}
for (int i = data.Count - sizeToCut; i < data.Count; i++)
{
newStat.Add(data[data.Count - sizeToCut - 1]);
}
return newStat;
}
// quantize so that Q1 ~ Q3 is 10 buckets, and find the bucket with the most values in it
// then recurse if there's still a lot of points in our largest bucket
// if there are 2 possible answer, we return the lowest one
public double GetMode()
{
double bucketSize = 0.1 * (GetQuantile(.75) - GetQuantile(.25));
if (bucketSize <= 0) return Median;
double result = 0;
int maxNbPoints = 0;
int i = 0;
int oldI = 0;
for (double d = Minimum + bucketSize; i < data.Count; d += bucketSize)
{
while (i < data.Count && data[i] < d) { i++; }
if (i - oldI > maxNbPoints) { maxNbPoints = i - oldI; result = d - bucketSize / 2; }
oldI = i;
}
OfflineUnivariateStat newStat = new OfflineUnivariateStat();
for (int j = 0; j < data.Count; j++)
{
if (data[j] > result + 3 / 2 * bucketSize)
break;
if (data[j] >= result - 3 / 2 * bucketSize)
newStat.Add(data[j]);
}
if (maxNbPoints > 1000)
return newStat.GetMode();
else
return newStat.Median;
}
// remove parts of a sample at the high and low end
public OfflineUnivariateStat Trim(double percent = 0.25)
{
OfflineUnivariateStat newStat = new OfflineUnivariateStat();
int sizeToCut = (int)(data.Count * percent);
for (int i = sizeToCut; i < data.Count - sizeToCut; i++)
{
newStat.Add(data[i]);
}
return newStat;
}
// breakdown point: 0.29
public double GetHodgesLehmann()
{
OfflineUnivariateStat newStat = new OfflineUnivariateStat();
for (int i = 0; i < data.Count; i++)
{
for (int j = i; j < data.Count; j++)
{
newStat.Add(data[i] + data[j]);
}
}
return 0.5 * newStat.Median;
}