Geodesic
Comparison of Sampling Schemes with and without Replacement
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 195-205

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An urn contains colored balls, $a$ balls of each of $N$ different colors. The balls are drawn sequentially and equiprobably, one ball at a time, and then each drawn ball drawn is either returned to the urn (sampling with replacement) or left outside the urn (sampling without replacement). The drawing continues until some $k$ colors are drawn at least $m$ times each. Observable statistics are the numbers $\mu_r$, $r=1,2,\dots$, of colors that have appeared precisely $r$ times each by the stopping time. The asymptotic behavior as $N\to\infty$ of these values for each of the two sampling models is studied; the possibility of their use for identifying the model is discussed. 
@article{MZM_2003_73_2_a3,
     author = {G. I. Ivchenko},
     title = {Comparison of {Sampling} {Schemes} with and without {Replacement}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {195--205},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a3/}
}
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G. I. Ivchenko. Comparison of Sampling Schemes with and without Replacement. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 195-205. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a3/