Distribution evaluation problem - Updated

Hi there! Please help me to solve the next problem

Imagine there is a continuous distribution D, and we need to evaluate its parameters (most probably it's left-skewed). What we know is that the range of random variable = [0,n].
We can take a sample A of limited size m, which obeys distribution D, and repeat the next procedure: for each element Ai from A you can choose a number Bi, and know, if Ai is larger then Bi or not. Looks like this:

for example n = 1000, m = 100

1. A1 = 156, but we don't know this
I chose B1 to be 500.
Output: A1<500

2. A2 = 678
I choose B2 to be 235
Output: A2>235


100. A100 = 823
I choose B100 to be 647
Output: A100>647

I need to come up with an algorithm of evaluating distribution D
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Ambassador to the humans
I'll be honest. I don't think you did a good job describing your problem in a way that others can follow. Can you give it another go?

Also are you sure you meant left skewed? Right skewed for what you were describing would make much more sense to me...


Ambassador to the humans
Do you know anything else about the distribution? Maybe some functional form for probability mass function? Is n known?
I suppose that density of the distribution should look something like this.
Also n varies from experiment to experiment, it can be 1000, 2000, 5000
Worth noting that I'm quite limited with sample size, let me say 100 is what I expect
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N is fixed and known during the whole experiment. I'm just saying that I need to run a couple of such experiments.
I don't know the functional form.
I would be absolutely satisfied even having a histogram of discrete values of D