Theo1 confidence intervals [frequency stability measurement applications]

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 /spl sigma//sub y/(/spl tau/) (Adev) in estimating long-term frequency stability, in that: (1) it can evaluate frequency stability at averaging times 50% longer 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.