  Extending the argument of Ref.\citen{[4]} to the long-range spectral
statistics of classically integrable quantum systems, we examine the level
number variance, spectral rigidity and two-level cluster function. These
observables are obtained by applying the approach of Berry and Robnik\cite{[0]}
and the mathematical framework of Pandey \cite{[2]} to systems with infinitely
many components, and they are parameterized by a single function $\bar{c}$,
where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$
indicates deviations from Poisson statistics. This implies that even when the
spectral components are statistically independent, non-Poissonian spectral
statistics are possible.
