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

Statistics Theory 2021-04-27 v2 Computation Statistics Theory

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.

Keywords

Cite

@article{arxiv.2103.11712,
  title  = {Approximation to probability density functions in sampling distributions based on Fourier cosine series},
  author = {Shigekazu Nakagawa and Hiroki Hashiguchi and Yoko Ono},
  journal= {arXiv preprint arXiv:2103.11712},
  year   = {2021}
}

Comments

14 pages, 2 figures

R2 v1 2026-06-24T00:24:58.363Z