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\subsubsection{Error metric and optimal threshold}  The functions that used to  fit the background provide  also return an estimation of a goodness-of-fit estimator   computed on  the quality basis  of the fit, computed as the distance empirical distribution function (EDF)~\cite{Stephens1974,Parr1980}.   The ``distance''  between the empirical  \href{http://en.wikipedia.org/wiki/Cumulative\_distribution\_function}{cumulative EDF and the theoretical (i.e. exponential) cumulative  distribution function}  (CDF) represent  and fitted CDF. indicator of the quality of fit.  Two different distance metrics can be returned. returned by the background fitting functions.  The first is the \href{http://en.wikipedia.org/wiki/Kolmogorov\%E2\%80\%93Smirnov\_test}{Kolgomorov-Smirnov}  statistics (the Kolgomorov-Smirnov statistics, which uses the  maximum of the difference between the empirical and the  fitted CDF) EDF  and the theoretical distribution. The  second is the \href{http://en.wikipedia.org/wiki/Cram\%C3\%A9r\%E2\%80\%93von\_Mises\_criterion}{Cramér Cramér  von Mises} Mises  statistics corresponding to the integral of the squared residuals  (see the code \href{https://github.com/tritemio/FRETBursts/blob/master/fretbursts/background.py#L41}{here}). for more details,  \href{https://github.com/tritemio/FRETBursts/blob/master/fretbursts/background.py#L41}{link}).  In principle, the optimal interphoton-delay  threshold minimizes will minimize  the error metric. This approach is implemented by the function \href{http://fretbursts.readthedocs.org/en/latest/plugins.html#fretbursts.burstlib\_ext.calc\_bg\_brute}{calc\_bg\_brute}  in the  \href{http://fretbursts.readthedocs.org/en/latest/plugins.html}{burstlib\_ext module} and can be used  in cases when \verb|calc_bg_brute|  (\href{http://fretbursts.readthedocs.org/en/latest/plugins.html#fretbursts.burstlib\_ext.calc\_bg\_brute}{link}) which performs  a user wants brute-force search in order  to extract find  the most accurate estimation optimal threshold.  This level  of sofistication in estimation the  background rates. rates is not  necessary under typical circumstances, as the difference between an optimal threshold  and a manually (or euristically) choosen one is negligible in most practical cases.