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.
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