We give a simple and precise approximation to probability density functions in sampling distributions based on Fourier cosine series. After clarifying the required conditions, two examples are illustrated. One is the distribution of a sum of random variables uniformly distributed as the probability density function has an explicit expression. The other is the distribution of sample skewness of random variables normally distributed as the probability density function has no explicit expression.

翻译：我们给出基于 Fourier cosine 序列样本分布的概率密度函数简单精确的近似值。 在澄清所需条件后, 举两个示例。 一个是随机变量总和的分布, 因为概率密度函数有明确的表达式。 另一个是随机变量样本的分布, 随机变量通常分布为概率密度函数没有明确的表达式。