  We introduce the position-dependent probability distribution function (PDF)
of the smoothed matter field as a cosmological observable. In comparison to the
PDF itself, the spatial variation of the position-dependent PDF is simpler to
model and has distinct dependence on cosmological parameters. We demonstrate
that the position-dependent PDF is characterized by variations in the local
mean density, and we compute the linear response of the PDF to the local
density using separate universe N-body simulations. The linear response of the
PDF to the local density field can be thought of as the linear bias of regions
of the matter field selected based on density. We provide a model for the
linear response, which accurately predicts our simulation measurements. We also
validate our results and test the separate universe consistency relation for
the local PDF using global universe simulations. We find excellent agreement
between the two, and we demonstrate that the separate universe method gives a
lower variance determination of the linear response.
