Theo1 Confidence Intervals

Published

August 23, 2004

Author(s)

T Tasset, David A. Howe, Donald B. Percival

Abstract

Theoretical variance #1 (Theo1) has been developed at NIST to improve the estimation of long-term frequency stability. Its square-root (Theo1-dev) has two significant improvements over the Allan deviation XX called ¿Adev" in estimlating long-term frequency stability in that (1) it can evaluate frequency stability at averaging times 50 % longe'r than those of Adev and (2) it can estimate frequency stability with greater confidence than any other estimator. We discuss a method for determining the exact confidence intervals of Theo1, particularly useful for small sample sizes, using analytic techniques. The confidence intervals of Theo1 are narrower and less skewed ( more symmetric) than confidence intervals based on chi-square.

Proceedings Title

Proc. IEEE Intl. Ultrasonics, Ferroelectrics, and Frequency Control Anniversary Joint Conf.

Conference Dates

August 23-27, 2004

Conference Location

, USA

Conference Title

IEEE Intl. Ultrasonics, Ferroelectrics, and Frequency Control Conf.

Pub Type

Conferences

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Keywords

Allan variance, Chi-square, confidence interval, distribution function, frequency stabilization, frequency standard, Theo1, TheoH

Citation

Tasset, T. , Howe, D. and Percival, D. (2004), Theo1 Confidence Intervals, Proc. IEEE Intl. Ultrasonics, Ferroelectrics, and Frequency Control Anniversary Joint Conf., , USA, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50161 (Accessed October 10, 2025)