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arXiv · 2103.11712

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

Shigekazu Nakagawa·Hiroki Hashiguchi·Yoko Ono
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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.

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Shigekazu Nakagawa, Hiroki Hashiguchi, Yoko Ono. 2021-03-22. Approximation to probability density functions in sampling distributions based on Fourier cosine series. https://arxiv.org/abs/2103.11712

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