算法--樣本方差、樣本標准差、方差、標准方差與加權平均

樣本方差與樣本標准差

 1、定義：樣本中各數據與樣本平均數的差的平方和的平均數叫做樣本方差；樣本方差的算術平方根叫做樣本標准差。

      注：樣本方差和樣本標准差都是衡量一個樣本波動大小的量，樣本方差或樣本標准差越大，樣本數據的波動就越大。

標准差與標准方差

1、定義：方差是各個數據與平均數之差的平方和的平均數。在概率論和數理統計中，方差用來度量隨機變量和其數學期望（即均值）之間的偏離程度。標准差在概率統計中最常使用作為統計分布程度上的測量。標准差定義為方差的算術平方根，反映組內個體間的離散程度。

加權平均

1、定義：加權平均數（weighted average）是不同比重數據的平均數，就是把原始數據按照合理的比例來計算。

 

算法代碼如下：

        public static double StandardDeviation(this IList<double> source)
        {
            if (source == null)
            {
                throw new ArgumentNullException("source");
            }

            if (source.Count == 0)
            {
                return double.NaN;
            }

            double variance = source.Variance();

            return Math.Sqrt(variance);
        }

        public static double SampleStandardDeviation(this IList<double> source)
        {
            if (source == null)
            {
                throw new ArgumentNullException("source");
            }

            if (source.Count == 0 || source.Count == 1)
            {
                return double.NaN;
            }

            double variance = source.SampleVariance();

            return Math.Sqrt(variance);
        }

        public static double Variance(this IList<double> source)
        {
            if (source == null)
            {
                throw new ArgumentNullException("source");
            }

            if (source.Count == 0)
            {
                return double.NaN;
            }

            int count = source.Count();
            double deviation = CalculateDeviation(source, count);

            return deviation / count;
        }

        public static double SampleVariance(this IList<double> source)
        {
            if (source == null)
            {
                throw new ArgumentNullException("source"); ;
            }

            if (source.Count == 0 || source.Count == 1)
            {
                return double.NaN;
            }

            int count = source.Count();
            double deviation = CalculateDeviation(source, count);

            return deviation / (count - 1);
        }

        public static double WeightedAverage(this IList<double> source, IList<double> factors)
        {
            if (source == null)
            {
                throw new ArgumentNullException("source");
            }

            if (source.Count != factors.Count)
            {
                throw new ArgumentException("source count is not equal to factors count.");
            }

            if (source.Count == 0)
            {
                return double.NaN;
            }

            double sum = factors.Sum();

            if (sum == 0)
            {
                return double.NaN;
            }

            double weight = 0;

            for (int index = 0; index < factors.Count; index++)
            {
                weight += source[index] * (factors[index] / sum);
            }

            return weight;
        }

        private static double CalculateDeviation(IList<double> source, int count)
        {
            double avg = source.Average();
            double deviation = 0;

            for (int index = 0; index < count; index++)
            {
                deviation += (source[index] - avg) * (source[index] - avg);
            }

            return deviation;
        }

以上在金融方面用得比較多.....