public WelchResult IsGreater(double[] x, double[] y, Threshold threshold = null)
{
int n1 = x.Length, n2 = y.Length;
if (n1 < 2)
{
throw new ArgumentException("x should contains at least 2 elements", nameof(x));
}
if (n2 < 2)
{
throw new ArgumentException("y should contains at least 2 elements", nameof(y));
}
Moments xm = Moments.Create(x), ym = Moments.Create(y);
double v1 = xm.Variance, v2 = ym.Variance, m1 = xm.Mean, m2 = ym.Mean;
threshold = threshold ?? RelativeThreshold.Default;
double thresholdValue = threshold.GetValue(x);
double se = Math.Sqrt(v1 / n1 + v2 / n2);
double t = ((m1 - m2) - thresholdValue) / se;
double df = (v1 / n1 + v2 / n2).Sqr() /
((v1 / n1).Sqr() / (n1 - 1) + (v2 / n2).Sqr() / (n2 - 1));
double pValue = 1 - new StudentDistribution(df).Cdf(t);
return(new WelchResult(t, df, pValue, threshold));
}
public Histogram Build(IReadOnlyList <double> values)
{
var moments = Moments.Create(values);
double binSize = GetOptimalBinSize(values.Count, moments.StandardDeviation);
if (Math.Abs(binSize) < 1e-9)
{
binSize = 1;
}
return(Build(values, binSize));
}
/// <summary>
/// Determines whether the sample mean is different from a known mean
/// </summary>
/// <remarks>Should be consistent with t.test(x, mu = mu, alternative = "greater") from R </remarks>
public OneSidedTestResult IsGreater(double[] sample, double value, Threshold threshold = null)
{
var moments = Moments.Create(sample);
double mean = moments.Mean;
double stdDev = moments.StandardDeviation;
double n = sample.Length;
double df = n - 1;
threshold = threshold ?? RelativeThreshold.Default;
double t = (mean - value) /
(stdDev / Math.Sqrt(n));
double pValue = 1 - new StudentDistribution(df).Cdf(t);
return(new OneSidedTestResult(pValue, threshold));
}
public static double Calculate([NotNull] double[] values)
{
try
{
var clearedValues = TukeyOutlierDetector.Create(values).WithoutAllOutliers(values).ToList();
int n = clearedValues.Count;
var quartiles = Quartiles.Create(clearedValues);
var moments = Moments.Create(clearedValues);
double mValue = 0;
double binSize = AdaptiveHistogramBuilder.GetOptimalBinSize(n, moments.StandardDeviation);
if (Abs(binSize) < 1e-9)
{
binSize = 1;
}
while (true)
{
var histogram = HistogramBuilder.Adaptive.Build(clearedValues, binSize);
var x = new List <int> {
0
};
x.AddRange(histogram.Bins.Select(bin => bin.Count));
x.Add(0);
int sum = 0;
for (int i = 1; i < x.Count; i++)
{
sum += Abs(x[i] - x[i - 1]);
}
mValue = Max(mValue, sum * 1.0 / x.Max());
if (binSize > quartiles.Max - quartiles.Min)
{
break;
}
binSize *= 2.0;
}
return(mValue);
}
catch (Exception)
{
return(1); // In case of any bugs, we return 1 because it's an invalid value (mValue is always >= 2)
}
}
public static double Calc([NotNull] Sample x, [NotNull] Sample y)
{
Assertion.NotNull(nameof(x), x);
Assertion.NotNull(nameof(y), y);
if (x.Count < 2)
{
throw new ArgumentOutOfRangeException(nameof(x), $"{nameof(x)} should contain at least 2 elements");
}
if (y.Count < 2)
{
throw new ArgumentOutOfRangeException(nameof(y), $"{nameof(y)} should contain at least 2 elements");
}
int nx = x.Count;
int ny = y.Count;
var mx = Moments.Create(x);
var my = Moments.Create(y);
double s = Math.Sqrt(((nx - 1) * mx.Variance + (ny - 1) * my.Variance) / (nx + ny - 2));
return((my.Mean - mx.Mean) / s);
}
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);
}