Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the modes of the negative binomial distribution of order k,
  type I   Upper and lower bounds are derived for the mode(s) of the negative binomial
distribution of order k, type I, with parameters r and p, which are employed to
establish an explicit formula for the mode(s) in terms of r and k when p equals
0.5. It is also shown as a direct consequence of the upper bound alone that the
mode is k when r equals 1. The derivation of the bounds is based on a known
recurrence relation satisfied by the probability mass function of the
distribution.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
9
The categories of this paper are: nlin