We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the distribution of the sum of uniformly distributed random variables, and the distribution of sample skewness drawn from a normal population. The probability density function of the first example can be explicitly expressed, but that of the second example has no explicit expression.

翻译：我们得出基于 Fourier cosine 系列样本分布的概率密度函数简单而精确的近似值。 在澄清了所需条件之后,我们用两个例子来说明近似值:统一分布随机变量总和的分布,以及从正常人群中提取的样本偏差的分布。第一个例子的概率密度函数可以明确表达,但第二个例子的概率密度函数没有明确表达。