public Statistics(IEnumerable <double> values)
{
OriginalValues = values.Where(d => !double.IsNaN(d)).ToArray();
SortedValues = OriginalValues.OrderBy(value => value).ToArray();
N = SortedValues.Count;
if (N == 0)
{
throw new InvalidOperationException("Sequence of values contains no elements, Statistics can't be calculated");
}
if (N == 1)
{
Q1 = Median = Q3 = SortedValues[0];
}
else
{
double GetMedian(IReadOnlyList <double> x) => x.Count % 2 == 0
? (x[x.Count / 2 - 1] + x[x.Count / 2]) / 2
: x[x.Count / 2];
Median = GetMedian(SortedValues);
Q1 = GetMedian(SortedValues.Take(N / 2).ToList());
Q3 = GetMedian(SortedValues.Skip((N + 1) / 2).ToList());
}
Min = SortedValues.First();
Mean = SortedValues.Average();
Max = SortedValues.Last();
InterquartileRange = Q3 - Q1;
LowerFence = Q1 - 1.5 * InterquartileRange;
UpperFence = Q3 + 1.5 * InterquartileRange;
AllOutliers = SortedValues.Where(IsOutlier).ToArray();
LowerOutliers = SortedValues.Where(IsLowerOutlier).ToArray();
UpperOutliers = SortedValues.Where(IsUpperOutlier).ToArray();
Variance = N == 1 ? 0 : SortedValues.Sum(d => Math.Pow(d - Mean, 2)) / (N - 1);
StandardDeviation = Math.Sqrt(Variance);
StandardError = StandardDeviation / Math.Sqrt(N);
Skewness = CalcCentralMoment(3) / StandardDeviation.Pow(3);
Kurtosis = CalcCentralMoment(4) / StandardDeviation.Pow(4);
ConfidenceInterval = new ConfidenceInterval(Mean, StandardError, N);
Percentiles = new PercentileValues(SortedValues);
}
/// <summary>
/// Determine if either x or y values are sorted; if neither, sort x.
/// </summary>
private void DetermineSorted()
{
SortedToUnsorted = Enumerable.Range(0, xTransformed.Length).ToArray();
if (IsSorted(xTransformed))
{
TransformedSorted = xTransformed;
SortedValues = SortedValues.X;
}
else if (IsSorted(yTransformed))
{
TransformedSorted = yTransformed;
SortedValues = SortedValues.Y;
}
else
{
TransformedSorted = (double[])xTransformed.Clone();
Array.Sort(TransformedSorted, SortedToUnsorted);
}
}
public Statistics(IEnumerable <double> values)
{
OriginalValues = values.Where(d => !double.IsNaN(d)).ToArray();
SortedValues = OriginalValues.OrderBy(value => value).ToArray();
N = SortedValues.Count;
if (N == 0)
{
throw new InvalidOperationException("Sequence of values contains no elements, Statistics can't be calculated");
}
var quartiles = Quartiles.FromSorted(SortedValues);
Min = quartiles.Min;
Q1 = quartiles.Q1;
Median = quartiles.Median;
Q3 = quartiles.Q3;
Max = quartiles.Max;
InterquartileRange = quartiles.InterquartileRange;
var moments = Moments.Create(SortedValues);
Mean = moments.Mean;
StandardDeviation = moments.StandardDeviation;
Variance = moments.Variance;
Skewness = moments.Skewness;
Kurtosis = moments.Kurtosis;
var tukey = TukeyOutlierDetector.FromQuartiles(quartiles);
LowerFence = tukey.LowerFence;
UpperFence = tukey.UpperFence;
AllOutliers = SortedValues.Where(tukey.IsOutlier).ToArray();
LowerOutliers = SortedValues.Where(tukey.IsLowerOutlier).ToArray();
UpperOutliers = SortedValues.Where(tukey.IsUpperOutlier).ToArray();
outlierDetector = tukey;
StandardError = StandardDeviation / Math.Sqrt(N);
ConfidenceInterval = new ConfidenceInterval(Mean, StandardError, N);
Percentiles = new PercentileValues(SortedValues);
}
public Statistics(IEnumerable <double> values)
{
OriginalValues = values.Where(d => !double.IsNaN(d)).ToArray();
SortedValues = OriginalValues.OrderBy(value => value).ToArray();
N = SortedValues.Count;
if (N == 0)
{
throw new InvalidOperationException("Sequence of values contains no elements, Statistics can't be calculated");
}
if (N == 1)
{
Q1 = Median = Q3 = SortedValues[0];
}
else
{
double GetMedian(IReadOnlyList <double> x) => x.Count % 2 == 0
? (x[x.Count / 2 - 1] + x[x.Count / 2]) / 2
: x[x.Count / 2];
Median = GetMedian(SortedValues);
Q1 = GetMedian(SortedValues.Take(N / 2).ToList());
Q3 = GetMedian(SortedValues.Skip((N + 1) / 2).ToList());
}
Min = SortedValues.First();
Max = SortedValues.Last();
InterquartileRange = Q3 - Q1;
LowerFence = Q1 - 1.5 * InterquartileRange;
UpperFence = Q3 + 1.5 * InterquartileRange;
AllOutliers = SortedValues.Where(IsOutlier).ToArray();
LowerOutliers = SortedValues.Where(IsLowerOutlier).ToArray();
UpperOutliers = SortedValues.Where(IsUpperOutlier).ToArray();
}
/// <summary>
/// Determine if either x or y values are sorted; if neither, sort x.
/// </summary>
private void DetermineSorted()
{
SortedToUnsorted = Enumerable.Range(0, xTransformed.Length).ToArray();
if (IsSorted(xTransformed))
{
TransformedSorted = xTransformed;
SortedValues = SortedValues.X;
}
else if (IsSorted(yTransformed))
{
TransformedSorted = yTransformed;
SortedValues = SortedValues.Y;
}
else
{
TransformedSorted = (double[])xTransformed.Clone();
Array.Sort(TransformedSorted, SortedToUnsorted);
}
}
/// <summary> /// Statistics for [1/X]. If Min is less then or equal to 0, returns null. /// </summary> public Statistics Invert() => CanBeInverted() ? new Statistics(SortedValues.Select(x => 1 / x)) : null;
[PublicAPI] public double CalcCentralMoment(int k) => SortedValues.Average(x => (x - Mean).Pow(k));
[PublicAPI] public double[] WithoutOutliers() => SortedValues.Where(value => !IsOutlier(value)).ToArray();