This page in a nutshell: An overwhelming majority of new users (80%) make their first edit within a day of registering, and 75% make it within one hour.
Data for a registered user's first edit ever -- which includes live and deleted edits -- was generated. This was then compared to the user's registration date. Note: because of legacy installations of MediaWiki, user registration data may be inaccurate prior to 2005. At that time, the software would sometimes record the date of a user's first edit as their registration date. However, this makes up a small percent of users given the massive growth in registration and editors in 2006-7.
The data for all users were then fitted to a Gaussian mixture model, a clustering technique that is able to separate lag observations in several classes (or components). We tried fitting a mixture of N=2,3, and 4 components. Estimation of the parameters of the model is performed via the Expectation Maximization algorithm (EM). The data are first transformed in logarithmic scale (base 10). If data are log-normally distributed, then we should see that the logarithm is distributed according to the normal distribution.