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

Approximation to probability density functions in sampling distributions based on Fourier cosine series