  We numerically study the volume density probability distribution function
(n-PDF) and the column density probability distribution function (Sigma-PDF)
resulting from thermally bistable turbulent flows. We analyze three-dimensional
hydrodynamic models in periodic boxes of 100pc by side, where turbulence is
driven in the Fourier space at a wavenumber corresponding to 50pc. At low
densities (n <= 0.6cm^-3) the n-PDF, is well described by a lognormal
distribution for average local Mach number ranging from ~0.2 to ~5.5. As a
consequence of the non linear development of thermal instability (TI), the
logarithmic variance of the distribution for the diffuse gas increases with M
faster than in the well known isothermal case. The average local Mach number
for the dense gas (n >= 7.1cm^-3) goes from ~1.1 to ~16.9 and the shape of the
high density zone of the n-PDF changes from a power-law at low Mach numbers to
a lognormal at high M values. In the latter case the width of the distribution
is smaller than in the isothermal case and grows slower with M. At high column
densities the Sigma-PDF is well described by a lognormal for all the Mach
numbers we consider and, due to the presence of TI, the width of the
distribution is systematically larger than in the isothermal case but follows a
qualitatively similar behavior as M increases. Although a relationship between
the width of the distribution and M can be found for each one of the cases
mentioned above, these relations are different form those of the isothermal
case.
