I'd like to fit a distribution (any you like) based on these requirements:
- Produces integer values (preferable but not required)
- Mean ($\mu$)=100
- Quantiles( 25%, 50%, 75%)=(6,39,200)
- Min=0; Max=~300 (but $\infty$ is acceptable);
Poisson fits criteria 1,2 and nearly 3, but not 4 by far. Lognormal... maybe
EXTRA info: value 0 is produced 8% of the time and 300 is produced 18%.
Is it possible to do something like this?