I think the most important question to ask is: how were the data points in the plot generated? That should provide some clue as to an appropriate function.
OK, that's helpful. There are multiple approaches you can take, depending on what you are ultimately trying to do. Is it interpolation between data points? If so, then you really don't need to fit a function to the entire data set, just the points in the vicinity of where you want to interpolate.
You could also fit the data points with a series of cubic splines, which would result in a smooth curve but wouldn't result in a single equation for all data points, but rather multiple equations depending on the value of x.
If you really need a single equation to fit all the data (hard to imagine why), one possibility is to fit an n-1 order polynomial to the n data points. Other options are least squares fitting to various functions (won't likely be an exact fit), but choosing the function to try is perhaps more art than science. Other than an exact polynomial fit, I know of no way to magically derive a function to model a set of data. Lots of trial and error. One possibility is some sort of exponential function like this:
Looking at the graph I think it could be a sum of 3 peaks of different width (at half the maximum height) and height. So maybe you should start by trying to model a single peak, maybe a normal distribution. But perhaps my guess is not too educated.
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The graph does show points marked with a point (or whatever), what do those points stand for?
How often did your run the experiment? Since the graph doesn't look like a normal distribution, the number of trials might to too low.
Could you post the actual values for the probability that you used for this graph (helps us "making" a formula).
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Originally Posted by hawk80
