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We present an experimental study of missing level statistics ofthree-dimensional chaotic microwave cavities. The investigation is reinforcedby the power spectrum of level fluctuations analysis which also takes intoaccount the missing levels. On the basis of our data sets we demonstrate thatthe power spectrum of level fluctuations in combination with short- andlong-range spectral fluctuations provides a powerful tool for the determinationof the fraction of randomly missing levels in systems that display wave chaossuch as the three-dimensional chaotic microwave cavities. The experimentalresults are in good agreement with the analytical expressions that explicitlytake into account the fraction of observed levels. We also show that in thecase of incomplete spectra with many unresolved states the above procedures mayfail. In such a case the random matrix theory calculations can be useful forthe determination of missing levels.

Missing level statistics and the power spectrum of level fluctuations analysis of three-dimensional chaotic microwave cavities