# Need guidance on types of stats or stat tests that can be done for simulation

1. Jul 25, 2011

### skyflashings

I will try to be brief, so please bear with me!

I have a Matlab program which simulates a particle's movement over time in a certain ocean. The details of this implementation aren't really important, but basically I create about ~300 particles near each other and place them at a certain place in the ocean and through time they get pushed around by the water's current and end up somewhere completely different.

The starting place for the simulation is chosen on a particular day, say January 1, 2008, and the particle is moved around for about 60 days time. I save the results, and then do the same thing starting on January 2, 2008, and so on. I can do this for the whole month of January, or even the whole year of 2008. The idea is I will end up having the ending positions of these particles and (hopefully) can see an area of where they generally tend to gravitate towards.

Here is the part where I would like some guidance. I took a basics stats course in college but I don't really remember too much. Using the resulting positions of the particles, can I form some kind of distribution that will fit the data? (I'm not even sure if that even makes sense in this case). Or do some other kind of interesting statistical thing to it other than say "X percent of the particles end up in this boxed region"....like, say, a histogram?

I would really appreciate any ideas or guidance. Thanks!

2. Jul 25, 2011

### pmsrw3

Let's see. Your particles will have a distribution in 2 dimensions? 3?

Yes, there are things you can do. Briefly, some of them are:

1) Calculate the mean position of a particle.
2) Calculate the spread of the particles. (In one dimension this would be one number, the standard deviation. In multiple dimensions it's a little more complicated.)
3) Check whether a multinormal distribution gives a good fit.
4) Histograms or density plots. Again, this is more complicated in multiple dimensions than 1. And, especially if the distribution is 3-dimensional, you may find that 300 particles is not enough.

There are many other things that could be done, but that's a start.

3. Jul 25, 2011

### skyflashings

Ah, sorry I didn't make that clear. It's in 2 dimensions (longitude and latitude).