Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling from a mixture of different groups of coupons   A collector samples coupons with replacement from a pool containing $g$
\textit{uniform} groups of coupons, where "uniform group" means that all
coupons in the group are equally likely to occur. For each $j = 1, \dots, g$
let $T_j$ be the number of trials needed to detect Group $j$, namely to collect
all $M_j$ coupons belonging to it at least once. We derive an explicit formula
for the probability that the $l$-th group is the first one to be detected
(symbolically, $P\{T_l = \bigwedge_{j=1}^g T_j\}$). We also compute the
asymptotics of this probability in the case $g=2$ as the number of coupons
grows to infinity in a certain manner. Then, in the case of two groups we focus
on $T := T_1 \vee T_2$, i.e. the number of trials needed to collect all coupons
of the pool (at least once). We determine the asymptotics of $E[T]$ and $V[T]$,
as well as the limiting distribution of $T$ (appropriately normalized) as the
number of coupons becomes very large.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn