Theo1 confidence intervals

Theoretical variance #1 (T (heo) over cap1) has been developed at NIST to improve the estimation of longterm frequency stability. Its square-root (T (heo) over cap1-dev) has two significant improvements over the Allan deviation sigma(y)(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 T (heo) over cap1, particularly useful for small sample sizes, using analytic techniques. The confidence intervals of T (heo) over cap1. are narrower and less skewed (more symmetric) than confidence intervals based oil chi-square.