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Approximation to probability density functions in sampling distributions based on Fourier cosine series (2103.11712v2)
Published 22 Mar 2021 in math.ST, stat.CO, and stat.TH
Abstract: 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.