# Distances between successive points - Statistical Test

I have a set of experimental data which comprises distances between successive points:

I also have a set of similar data that has been generated by a model that attempts to recapture the (biological) phenomenon behind the experimental distances.

An example of each set is here:

x-axis = No. of Distances (plotted in increasing size)
y-axis (logarithmic) = Distance size


I am not an accomplish statistician and was wondering what the best statistical test or approach would be to use in order to assess the agreement between these two sets of data? I effectively want to know how well the model recaptures the experimental data - the "closeness" of the data/fit.

EDIT: The most important parts of the data typically reside at the tails any test needs to be somewhat sensitive to this.

Any suggestions?

• Your graph is essentially Ripley's K function, just without dividing by the density of the point pattern. Commented Jul 4, 2015 at 22:54

$$\sup_{s \in \mathbb{R}} \left | \hat{F}_1(s) - \hat{F}_2(s) \right | ,$$
where if your two samples are $(x_1, x_2, \ldots, x_{n_1})$ and $(y_1, y_2, \ldots , y_{n_2})$ we define $\hat{F}_1(s) \equiv n^{-1}_1 \sum_{i=1}^{n_1} I(x_{i} \leq s)$ and $\hat{F}_2(s) \equiv n^{-1}_2 \sum_{i=1}^{n_2} I(y_{i} \leq s)$. So, each function tells what proportion of the sample is less than or equal to any value $s \in \mathbb{R}$, and then you calculate the largest difference between these functions. When this distance is large you conclude that the true distributions differ, and what constitutes "large" depends on how this value behaves when the distributions are in fact the same. Most statistical software packages will have a procedure for performing this test for you, so you shouldn't have to worry too much about these details. Do you have access to something like R or SAS? It may even be possible to run in Excel.
• I think the Anderson-Darling test is usually thought of as a one sample test, but I suppose it could be adapted to two samples. It does involve a weight function $w(x)$ which allows you to assign more weight to the tail if you wish, although then you have to think about how to define this function. I personally haven't used this test so can't really comment too much on it. Commented Jul 5, 2015 at 17:29