deletions | additions       diff --git a/Methodology Measures PET.tex b/Methodology Measures PET.tex  index bbd21d8..55aa3ec 100644  --- a/Methodology Measures PET.tex  +++ b/Methodology Measures PET.tex 
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Instantaneous surrogate safety indicators may be aggregated over time for each interaction (or user pair), over a given time interval for several road users and over space. Indicator distributions are generally shaped like Gamma distributions across the literature \cite{Ismail_2010,Autey_2012,St_Aubin_2013}. Quantifying collision risk based on any of the surrogate safety indicators is the remaining puzzle piece. Using a TTC threshold has been the traditional approach in traffic conflict techniques \cite{Svensson_2006}, correlating a number of interactions with minimum TTC below a threshold with an expected number of collisions, though this constitutes a significant loss of information \cite{Mohamed_2013} and this introduces assumptions in the model. One recent approach proposed a shifted gamma-generalised Pareto distribution model \cite{Zheng_2014}.   Nevertheless, some qualitative analysis is possible in some circumstances, for example with a continuous mass shift of a probability distribution function as demonstrated in Figure~\ref{fig:distro-comparison}. This approach has been tried in some early applications of the methodology, e.g. in \cite{Ismail_2010}, \cite{Autey_2012}, and in \cite{St_Aubin_2013}. Figure~\ref{fig:distro-comparison} also \cite{Ismail_2010,Autey_2012,St_Aubin_2013}. Figure~\ref{fig:distro-aggregation}  demonstrates three different TTC distribution aggregation methods as used to represent nearly 3 million TTC observations over the course of one day at a single site: i) all instantaneous indicator values (subject to over-sampling of low severity values as well as over-sampling by slower road users and longer corridors), ii) minimum value of time series per user pair, or iii) 15th percentile value of time series per user pair. The 15th percentile is a practical solution to ignoring outliers that may be introduced for influence the  maxima.