  We introduce a new powerful scan statistic and an associated test for
detecting the presence and pinpointing the location of a change point within
the distribution of a data sequence where the data elements take values in a
general separable metric space $(\Omega, d)$. These change points mark abrupt
shifts in the distribution of the data sequence. Our method hinges on distance
profiles, where the distance profile of an element $\omega \in \Omega$ is the
distribution of distances from $\omega$ as dictated by the data. Our approach
is fully non-parametric and universally applicable to diverse data types,
including distributional and network data, as long as distances between the
data objects are available. From a practicable point of view, it is nearly
tuning parameter-free, except for the specification of cut-off intervals near
the endpoints where change points are assumed not to occur. Our theoretical
results include a precise characterization of the asymptotic distribution of
the test statistic under the null hypothesis of no change points and rigorous
guarantees on the consistency of the test in the presence of change points
under contiguous alternatives, as well as for the consistency of the estimated
change point location. Through comprehensive simulation studies encompassing
multivariate data, bivariate distributional data and sequences of graph
Laplacians, we demonstrate the effectiveness of our approach in both change
point detection power and estimating the location of the change point. We apply
our method to real datasets, including U.S. electricity generation compositions
and Bluetooth proximity networks, underscoring its practical relevance.
