Distribution options?

I've run into a bit of problem, trying to figure out how to distribute products over different intervals with a simple formula.
So i'm hoping for some ideas how to tackle this problem.

The idea is that an number of products can be sent out a day. And they can arrive according to a distribution schedule.
Say product X will be sent out in batch and it will arrive on different days. The first day 60%, 2nd 25%, 3rd 10% and 4th 5%.
The next day you'll have another batch doing the same distribution.
For another product this might be a different distribution. And distributions can take up to several weeks.

I've added an example file for reference. The result part in the file is what the result should look like. But the formula is too labour intensive for changes or other products.

I've tried a matrix, but if it had 70 intervals, and several different products. It got too complex.
How would you tackle this? It feels like a complex problem, but the solution might be simple.
I'm hoping for a solution for with different distributions. But if you have a great idea with a single distribution schedule for different products i'm open to that suggestion.

All suggestions are appreciated.