  This paper investigates Distributed Hypothesis testing (DHT), in which a
source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is
available at the decoder only. Based on the received coded data, the receiver
aims to decide on the two hypotheses $H_0$ or $H_1$ related to the joint
distribution of $\mathbf{X}$ and $\mathbf{Y}$. While most existing
contributions in the literature on DHT consider i.i.d. assumptions, this paper
assumes more generic, non-i.i.d., non-stationary, and non-ergodic sources
models. It relies on information-spectrum tools to provide general formulas on
the achievable Type-II error exponent under a constraint on the Type-I error.
The achievability proof is based on a quantize-and-binning scheme. It is shown
that with the quantize-and-binning approach, the error exponent boils down to a
trade-off between a binning error and a decision error, as already observed for
the i.i.d. sources. The last part of the paper provides error exponents for
particular source models, \emph{e.g.}, Gaussian, stationary, and ergodic
models.
