  Usual approach to investigate the statistical properties of deterministically
thermostated systems is to analyze the regime of the system motion. In this
work the cumulant analysis is used to study the properties of the stationary
probability distribution function of the deterministically thermostated
harmonic oscillators. This approach shifts attention from the investigation of
the geometrical properties of solutions of the systems to the studying a
probabilistic measure. The cumulant apparatus is suitable for studying the
correlations of dynamical variables, which allows one to reveal the deviation
of the actual probabilistic distribution function from canonical one and to
evaluate it. Three different thermostats, namely the Nos\'e-Hoover,
Patra-Bhatacharya and Hoover-Holian ones, were investigated. It is shown that
their actual distribution functions are non-canonical because of nonlinear
coupling of the oscillators with thermostats. The problem of ergodicity of the
deterministically thermostated systems is discussed.
