a vector of length equal to the number of pools. The entries are weights. That means that their sume must be equal to one!
times
the times for which the distribution density is sought
Details
Given a system described by
the complete history of inputs $\mathbf{I}(t)$
for $t\in (t_{start},t_0)$
to all pools until time $t_0$
and
the cumulative output $O(t_0)$
of all pools at time $t_0$
the transit time density $\psi_{t_0}(T)$
of the systemat time $t_0$ is the probability density
with respect to $T$ implicitly defined by
$$\bar T_{t_0} = \int_0^{t-t_{start}} \psi_{t_0}(T) T \;dT$$
References
Manzoni, S., G.G. Katul, and A. Porporato. 2009. Analysis of soil carbon transit times and age distributions using network theories.
Journal of Geophysical Research-Biogeosciences 114, DOI: 10.1029/2009JG001070.