# methods for transit time distributions

### Description

According to getMeanTransitTime to we define the related density:

### Usage

 1 2 getTransitTimeDistributionDensity(object, inputDistribution, times) 

### Arguments

 object a protoDecompOp Object inputDistribution 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 ψ_{t_0}(T) of the system at time t_0 is the probability density with respect to T implicitly defined by

\bar T_{t_0} = \int_0^{t-t_{start}} ψ_{t_0}(T) T \;dT

### Author(s)

Carlos A. Sierra, Markus Mueller

### 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.

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