This idea courtesy of my brother.
Take a single day’s MAU measurement, and plot on a cumulative distribution function graph which days of the month each user first shows up.
Expected results should be a large volume on the 1st, 2nd, and/or 3rd day depending on when the weekend lines up, and then a steady slope the rest of the month for the pop ins that show up once or occasionally.
Actually, make it 28 days so it’s easy to figure out the week days.