public static decimal? StandardDeviation(this IEnumerable<decimal?> source);
public static decimal StandardDeviation(this IEnumerable<decimal> source);
public static double? StandardDeviation(this IEnumerable<double?> source);
public static double StandardDeviation(this IEnumerable<double> source);
public static float? StandardDeviation(this IEnumerable<float?> source);
public static float StandardDeviation(this IEnumerable<float> source);
public static double? StandardDeviation(this IEnumerable<int?> source);
public static double StandardDeviation(this IEnumerable<int> source);
public static double? StandardDeviation(this IEnumerable<long?> source);
public static double StandardDeviation(this IEnumerable<long> source);
public static decimal? StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, decimal?> selector);
public static decimal StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, decimal> selector);
public static double? StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, double?> selector);
public static double StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, double> selector);
public static float? StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, float?> selector);
public static float StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, float> selector);
public static double? StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, int?> selector);
public static double StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, int> selector);
public static double? StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, long?> selector);
public static double StandardDeviation<TSource>(this IEnumerable<TSource> source, Func<TSource, long> selector);

所有采用Nullable类型集合的重载仅在计算结果中包括实际值。例如：

public static double? StandardDeviation(this IEnumerable<double?> source)
{IEnumerable<double> values = source.AllValues();if (values.Any())return values.StandardDeviation();return null;
}

其AllValues方法是：

public static IEnumerable<T> AllValues<T>(this IEnumerable<T?> source) where T : struct
{Debug.Assert(source != null);return source.Where(x => x.HasValue).Select(x => (T)x);
}

public static double Variance(this IEnumerable<double> source)
{ int n = 0;double mean = 0;double M2 = 0;foreach (double x in source){n = n + 1;double delta = x - mean;mean = mean + delta / n;M2 += delta * (x - mean);}return M2 / (n - 1);
}

标准偏差

public static double StandardDeviation(this IEnumerable<double> source)
{ return Math.Sqrt(source.Variance());
}

中位数

public static double Median(this IEnumerable<double> source)
{ var sortedList = from number in source orderby number select number; int count = sortedList.Count(); int itemIndex = count / 2; if (count % 2 == 0) // Even number of items. return (sortedList.ElementAt(itemIndex) + sortedList.ElementAt(itemIndex - 1)) / 2; // Odd number of items. return sortedList.ElementAt(itemIndex);
}

模式

public static T? Mode<T>(this IEnumerable<T> source) where T : struct
{var sortedList = from number in sourceorderby numberselect number;int count = 0;int max = 0;T current = default(T);T? mode = new T?();foreach (T next in sortedList){if (current.Equals(next) == false){current = next;count = 1;}else{count++;}if (count > max){max = count;mode = current;}}if (max > 1)return mode;return null;
}

直方图

/// <summary>
/// Controls how the range of the bins are determined
/// </summary>
public enum BinningMode
{/// <summary>/// The minimum will be equal to the sequence min and the maximum equal to infinity/// such that:/// [min, min + binSize), [min * i, min * i + binSize), ... , [min * n, positiveInfinity)/// </summary>Unbounded,/// <summary>/// The minimum will be the sequence min and the maximum equal to sequence max/// The last bin will max inclusive instead of exclusive/// </summary>/// [min, min + binSize), [min * i, min * i + binSize), ... , [min * n, max]MaxValueInclusive,/// <summary>/// The total range will be expanded such that the min is/// less then the sequence min and max is greater then the sequence max/// [min - (binSize / 2), min - (binSize / 2) + binSize), /// [min - (binSize / 2) * i, min - (binSize / 2) * i + binSize), ... , /// [min - (bin / 2) * n, min + (binSize / 2))/// </summary>ExpandRange
}

创建直方图包括创建具有适当范围的Bin数组，然后确定每个范围内有多少个数据点。

public static IEnumerable<Bin> Histogram
(this IEnumerable<double> source, int binCount, BinningMode mode = BinningMode.Unbounded)
{if (source == null)throw new ArgumentNullException("source");if (!source.Any())throw new InvalidOperationException("source sequence contains no elements");var bins = BinFactory.CreateBins(source.Min(), source.Max(), binCount, mode);source.AssignBins(bins);return bins;
}

范围

public static double Range(this IEnumerable<double> source)
{return source.Max() - source.Min();
}

协方差

public static double Covariance(this IEnumerable<double> source, IEnumerable<double> other)
{int len = source.Count();double avgSource = source.Average();double avgOther = other.Average();double covariance = 0;for (int i = 0; i < len; i++)covariance += (source.ElementAt(i) - avgSource) * (other.ElementAt(i) - avgOther);return covariance / len;
}

皮尔逊卡方检验

public static double Pearson(this IEnumerable<double> source, IEnumerable<double> other)
{return source.Covariance(other) / (source.StandardDeviationP() * other.StandardDeviationP());
}

线性最小二乘法

public static LeastSquares LeastSquares(this IEnumerable<Tuple<double, double>> source)
{int numPoints = 0;double sumX = 0;double sumY = 0;double sumXX = 0;double sumXY = 0;foreach (var tuple in source){numPoints++;sumX += tuple.Item1;sumY += tuple.Item2;sumXX += tuple.Item1 * tuple.Item1;sumXY += tuple.Item1 * tuple.Item2;}if (numPoints < 2)throw new InvalidOperationException("Source must have at least 2 elements");double b = (-sumX * sumXY + sumXX * sumY) / (numPoints * sumXX - sumX * sumX);double m = (-sumX * sumY + numPoints * sumXY) / (numPoints * sumXX - sumX * sumX);return new LeastSquares(m, b);
}

均方根

public static double RootMeanSquare(this IEnumerable<double> source)
{if (source.Count() < 2)throw new InvalidOperationException("Source must have at least 2 elements");double s = source.Aggregate(0.0, (x, d) => x += Math.Pow(d, 2));return Math.Sqrt(s / source.Count());
}

使用代码

static void Main(string[] args)
{IEnumerable<int> data = new int[] { 1, 2, 5, 6, 6, 8, 9, 9, 9 };Console.WriteLine("Count = {0}", data.Count());Console.WriteLine("Average = {0}", data.Average());Console.WriteLine("Median = {0}", data.Median());Console.WriteLine("Mode = {0}", data.Mode());Console.WriteLine("Sample Variance = {0}", data.Variance());Console.WriteLine("Sample Standard Deviation = {0}", data.StandardDeviation());Console.WriteLine("Population Variance = {0}", data.VarianceP());Console.WriteLine("Population Standard Deviation = {0}", data.StandardDeviationP());Console.WriteLine("Range = {0}", data.Range());
}

...产生：

Count = 9
Average = 6.11111111111111
Median = 6
Mode = 9
Sample Variance = 9.11111111111111
Sample Standard Deviation = 3.01846171271247
Population Variance = 8.09876543209877
Population Standard Deviation = 2.8458329944146
Range = 8

兴趣点

public static T Range<T>(this IEnumerable<T> source)
{// error CS0019: Operator '-' cannot be applied to operands of type 'T' and 'T'return source.Max() - source.Min();
}

如果您查看框架类中由Average和Sum设置的模式(我在这里试图模拟)，他们对int，long，float，double和decimal进行枚举操作。为了避免过多的“复制、粘贴、修改代码和注释中的操作数类型”，T4模板非常方便。

  public static partial class EnumerableStats{<# var types = new List<string>(){"int", "long", "float", "double", "decimal"};foreach(var type in types){#> /// <summary>/// Computes the Range of a sequence of nullable <#= type #> values./// </summary>/// <param name="source">The sequence of elements.</param>/// <returns>The Range.</returns>public static <#= type #>? Range(this IEnumerable<<#= type #>?> source){IEnumerable<<#= type #>> values = source.AllValues();if (values.Any())return values.Range();return null;}/// <summary>/// Computes the Range of a sequence of <#= type #> values./// </summary>/// <param name="source">The sequence of elements.</param>/// <returns>The Range.</returns>public static <#= type #> Range(this IEnumerable<<#= type #>> source){return source.Max() - source.Min();}...etc etc...
<# } #>}