如何将这个峰度公式从java文档翻译成Ruby？

我对java文档中使用的奇怪峰度公式有一个问题：

---

峰度有四种稍有不同的定义：

过剩峰度是给定分布的峰度与正态分布的峰度之间的差异。偏差是被估计参数的期望值和真实值之间的差值。可以在和中找到更完整的解释

---

只能比较属于同一峭度版本的峭度值。nist网站（）解释了有偏的版本，Java文档（）解释了无偏的超额峰度。通常，这两个值根据您的结果而不同

您可以更好地查看Java类的源代码。

Computes the Kurtosis of the available values.

We use the following (unbiased) formula to define kurtosis:

kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]

where n is the number of values, mean is the Mean and std is the StandardDeviation

Note that this statistic is undefined for n < 4. Double.Nan is returned when there is not sufficient data to compute the statistic.

  def kurtosis
    return 0 if @values.length == 1
    cached_mean = mean
    n = @values.length.to_f

    rku = @values.sum { |x| (x - cached_mean)**4 }
    rkb = standard_deviation**4
    real_kurtosis = rku / rkb

    bk = (n * (n + 1)) / ((n - 1) * (n - 2) * (n - 3))
    ak = (3 * (n - 1)**2) / ((n - 2) * (n - 3))
    (bk * real_kurtosis) - ak
  end