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Screen Shot of my Mathematica Commands

I was using RandomSample with very skewed weights. I am asking for a random sample of 6 numbers 1 through 100 without replacement. In the screen shown, the weights for 1 through 6 are 100 000, with all others less then 1; hence, the RandomSample should return numbers 1 through 6 is a random order very very often. But it does not.

I have copied and pasted the commands shown.

Am I missing something? Or am I misunderstanding the RandomSample function? Or is this actually a bug?

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Please do not post images as code. Read the formatting FAQ in the Help section, and post actual code. – ciao Mar 5 '14 at 3:03

Definitely something interesting going on here.

c[x_] := Count[Table[RandomSample[{100000, 0, 1} -> {1, 2, 3}, 1], {x}], {3}]

DiscretePlot[c[x]/x, {x, 10, 400}]

enter image description here

Note that changing the zero weight to something greater than zero seems to give the expected behavior. Some experimentation seems to suggest that adding a zero weight in the presence of weights with large difference in scale causes other weights to be treated as equal.

I also notice that even when the weights are in the same ballpark odd stuff happens when we cross the 249 to 250 replication mark.

c2[x_] := Count[Table[RandomSample[{2, 0, 1, 2} -> {1, 2, 3, 4}, 1], {x}], {3}]
DiscretePlot[c[x]/x, {x, 10, 400}]

enter image description here

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It is clearly documented "The weights must be positive...", emphasis mine. – ciao Mar 5 '14 at 3:35
The threshold of 250 is likely due to auto-compilation in Table (which kicks in at precisely 250). – Szabolcs Mar 5 '14 at 3:41
This would explain why weights can't be zero, but if it's really so by design, RandomSample should give a warning, the same as it warns about negative weights. – Szabolcs Mar 5 '14 at 3:48
The weird behaviour at 250 is only with RandomSample, not RandomChoice, and only with integer weights, not with floating point weights. – Szabolcs Mar 5 '14 at 3:50
@Szabolcs I suspected auto-compilation as well. – Andy Ross Mar 5 '14 at 14:12

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