<s>
In	O
statistics	O
,	O
the	O
topic	O
of	O
location	B-General_Concept
testing	I-General_Concept
for	I-General_Concept
Gaussian	I-General_Concept
scale	I-General_Concept
mixture	I-General_Concept
distributions	I-General_Concept
arises	O
in	O
some	O
particular	O
types	O
of	O
situations	O
where	O
the	O
more	O
standard	O
Student	B-General_Concept
's	I-General_Concept
t-test	I-General_Concept
is	O
inapplicable	O
.	O
</s>
<s>
Specifically	O
,	O
these	O
cases	O
allow	O
tests	B-General_Concept
of	I-General_Concept
location	I-General_Concept
to	O
be	O
made	O
where	O
the	O
assumption	O
that	O
sample	O
observations	O
arise	O
from	O
populations	O
having	O
a	O
normal	O
distribution	O
can	O
be	O
replaced	O
by	O
the	O
assumption	O
that	O
they	O
arise	O
from	O
a	O
Gaussian	O
scale	O
mixture	O
distribution	O
.	O
</s>
<s>
This	O
means	O
that	O
if	O
we	O
test	O
the	O
null	O
hypothesis	O
that	O
the	O
center	O
of	O
a	O
Gaussian	O
scale	O
mixture	O
distribution	O
is	O
0	O
,	O
say	O
,	O
then	O
tnG(x )	O
(	O
x≥0	O
)	O
is	O
the	O
infimum	O
of	O
all	O
monotone	O
nondecreasing	O
functions	O
u(x )	O
≥	O
1/2	O
,	O
x≥0	O
such	O
that	O
if	O
the	O
critical	O
values	O
of	O
the	O
test	O
are	O
u−	O
1(1α )	O
,	O
then	O
the	O
significance	B-General_Concept
level	I-General_Concept
is	O
at	O
most	O
α≥	O
1/2	O
for	O
all	O
Gaussian	O
scale	O
mixture	O
distributions	O
[	O
tGn(x )	O
=	O
1tGn(x )	O
,	O
for	O
x	O
<	O
0 ]	O
.	O
</s>
