An increasing probability density function? Could anyone come up with a probability density function which is:


*

*supported on [1,∞) (or [0,∞))

*increasing

*discrete


I was having the same question, but in a bounded environment, so the distribution would be increasing with support a and b. It grows like a slow exponential, actually is the the distribution of the following:
Take N repetitions of 4 uniformly generated values between A and B. Make the histogram of the max in each repetition. You have something increasing that is not linear, it would be a kind of low speed growing exponential.
