Spectrum. I. Statistical Analysis %U http://dl.begellhouse.com/journals/0632a9d54950b268,687fe1c30cb4c059,04d7f13608595227.html %V 66 %X Statistical analysis of oscillations in SHF cavity resonator filled with random dielectric heterogeneities is performed. It is shown that the heterogeneities having negligibly small dissipative losses and result in essential shift and widening of spectral lines. We relate this effect to stochastic intermode wave scattering on heterogeneities. It is supplementary to dissipative widening caused by ohmic losses. The shift and widening of each spectral line depend essentially on frequency interval between this line and nearest lines of the spectrum. On increasing the interval, the influence of heterogeneities reduces substantially. This results in essential spectrum rarefaction. The rarefaction is due to the fact that solitary spectral lines are to minor extent subjected to the influence of heterogeneities and preserve their high quality factors. At the same time, the