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March, 1973 A General Method for the Approximation of Tail Areas
D. F. Andrews
Ann. Statist. 1(2): 367-372 (March, 1973). DOI: 10.1214/aos/1176342376

Abstract

For a density function $f(x)$, the tail area $\alpha(x) = \int^\infty_x f(x) dx,$ may be approximated by $\hat{\alpha}(x) = \frac{f(x)}{g(x)} \cdot (K - 1)^{-1}\cdot\big\{1 + \frac{1}{2} \big(\frac{g'(x)}{g^2(x)} - (K)\big)\big\},$ where $g(x) = f(x)/f'(x)$, and $K = \lim_{x\rightarrow\infty} \{g'(x)/g^2(x)\}$. The formula requires only one constant and three function evaluations; $g$ and $g'$ are typically elementary functions. Such approximations are useful for programmed calculators or very small computers where only a few constants can be stored. The accuracy of the approximation is calculated for some common distributions. The approximation is very accurate for a large class of distributions.

Citation

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D. F. Andrews. "A General Method for the Approximation of Tail Areas." Ann. Statist. 1 (2) 367 - 372, March, 1973. https://doi.org/10.1214/aos/1176342376

Information

Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0254.60002
MathSciNet: MR353539
Digital Object Identifier: 10.1214/aos/1176342376

Subjects:
Primary: 65D20

Rights: Copyright © 1973 Institute of Mathematical Statistics

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