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I'm looking for one specific sampling method that decides about inclusion probability of each item regardless of existence of other elements. As an example given 0.5 as the inclusion probability, it toss a coin for each element to decide about its inclusion.

This is different from fixed size sampling methods like sampling with replacement and without replacement as in this method only inclusion probability is provided and not the sample size.

Now I need more information about this method like the name of method, and the probability of having different sizes for the sample.

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  • $\begingroup$ Do you know what a binomial distribution is? $\endgroup$ Aug 9, 2015 at 7:41
  • $\begingroup$ Ahan, Thanks I guess that is what I'm looking for. I will check it out. :) Thanks $\endgroup$ Aug 9, 2015 at 7:41
  • $\begingroup$ It has its own wikipedia page. Anyway it is a descrete probability distribution over the number of successes in a series of independant binary yes/no trials where the probability of "yes" is some constant between 0 and 1. It may be what you want. $\endgroup$ Aug 9, 2015 at 7:48
  • $\begingroup$ Thanks. I only saw your first comment that had a typo. Thanks again. I guess it is really close to what I'm looking. I stuck badly but now at least I have something to start researching on ... $\endgroup$ Aug 9, 2015 at 7:50
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    $\begingroup$ If the binomial distribution does not work, you can edit your question to something like..."I would use a binomial distribution but for reasons X,Y,and Z" and a user on this cite would probably be able to offer more help or refer you somewhere helpful. $\endgroup$ Aug 9, 2015 at 7:55

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This method is called Poisson sampling (or sometimes Haje'k Poisson sampling after the statistician who first described it in detail). The name comes from the simple fact that the sample size is random, and for probability of selection invariant across units, the sample size is binomial (and hence for small probabilities of selection, which is often the case, is approximately Poisson). The first reference on Google does not seem too bad.

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