We will denote as ``X'' a population of m registered speakers:
For scoring purposes, we will consider a set of test utterances. We will use the term genuine test utterances for those which correspond to registered speakers, and the term impostor test utterances for those which are treated as belonging to impostor speakers. Note that the same speech segment can be used as a genuine utterance and as an impostor utterance, in some test configurations. Therefore, different notations can correspond to the same speech utterance.
Each registered speaker 
is supposed to have produced 
genuine test utterances , the set of which will be denoted as ``
'':
where superscript k denotes the 
test utterance of speaker .
In the rest of this chapter, we will denote as c the total number of
genuine test utterances , and as 
the proportion of utterances
belonging to speaker in the test set , that is:
With the convention:
we will denote:
Integer 
is the number of registered speakers for which there is at
least one genuine test utterance .
Finally, we will denote as M the set of male registered speakers, as
F the set of female registered speakers and as
and 
the
respective number of male and female registered speakers for which there is at
least one genuine test utterance .
In the most general case, the whole set of impostor test utterances
can be divided in subsets corresponding to one among n impostors
using the system with a claimed identity
. Hence the general notation
to denote the set of 
impostor test utterances produced by impostor 
claiming he is .
Similarly to genuine test utterances, we will denote as d the total
number of impostor utterances, and as 
the
proportion of impostor tests by impostor against registered
speaker , that is:
We will also write:
When the identity of impostors is not a relevant factor (or is
unknown), subscript j can be dropped, and 
denotes the impostor attempt against registered speaker
(
). Conversely, in open-set
speaker identification , impostors do not claim a particular identity;
they just try to be identified as one of the registered speakers ,
whoever this speaker may be. In this case, subscript 
can
be dropped, and 
denotes the impostor attempt
by impostor (
). If,
moreover, the impostor's identity does not matter, subscript j can
also be dropped, and 
simply denotes the impostor
attempt (
).
With the conventions:
 | if |  | and |  | otherwise |
 | if |  | and |  | otherwise |
 | if |  | and |  | otherwise |
we will write:
and
Integer 
is the number of impostors for which there is
at least one test utterance against registered speaker , integer
represents the number of registered speakers against which
there is at least one test utterance from impostor , 
is the
number of impostors from which there is at least one impostor test utterance,
is the number of registered speakers against which there is at
least one impostor test utterance , and 
denotes the total number of
couples 
for which there is at least one impostor test
utterance (from against ).
Finally, we will denote as 
the set of male impostor speakers, as 
the set of female impostor speakers, and
: the number of male registered speakers against which there is at least one impostor test utterance
: the number of female registered speakers against which there is at least one impostor test utterance
: the number of couples 
for which there is at least one impostor test utterance (from against , being a male speaker)
: the number of couples 
for which there is at least one impostor test utterance (from against , being a female speaker)