What distribution family would best fit this graph? Sorry if this type of question is not kosher. I'm new around here, so please forgive me.
Anyway, I have a dataset that describes the probability that users will like certain articles from my corpus (with 5 articles chosen randomly and graphed below. Along the x axis are individual users, and along the y-axis their score. The users are sorted by score.)
I'm looking to fit a distribution to each line, but am unsure of which one to choose that would likely best these lines. I was thinking of using an exponential distribution? But there's a lot of information that exponential probably would not capture here. Does anyone have a good idea?
EDIT: I will update my title to include the name of a reasonable distribution so that this question will be more searchable and others would possibly learn from it in the future.

 A: To many statisticians, information like this would usually be thought of as an empirical CDF:

with the scores on the x-axis, and the proportion of people scoring it less than or equal to a given x-value on the y-axis (that is, your x-axis ranks become scaled to proportions of people scoring no more than the person with that rank, and then becomes the new y-axis).
But it's sometimes difficult to identify good approximating distributions from the ECDF; it might be easier to look initially at some other displays (histograms with plenty of bins, kernel density estimates, Q-Q plots or other distributional plots.
You don't say what the range of possible scores is, but I presume they're bounded. If so, a scaled beta distribution might be a reasonable starting model:

As you see, with appropriate choices for the 4 parameters (I didn't try to fit these, just tried some values roughly in the right region), they can look quite similar to at least 4 of the 5 distributions you have there. However, they're probably not suitable in general. Mixture distributions might get you further along.
On the other hand you have a lot of data, so the empirical distribution probably has all you need to answer all kinds of questions about the data.
