<s>
In	O
statistics	O
,	O
minimum	B-General_Concept
chi-square	I-General_Concept
estimation	I-General_Concept
is	O
a	O
method	O
of	O
estimation	O
of	O
unobserved	O
quantities	O
based	O
on	O
observed	O
data	O
.	O
</s>
<s>
In	O
certain	O
chi-square	O
tests	O
,	O
one	O
rejects	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
about	O
a	O
population	O
distribution	O
if	O
a	O
specified	O
test	O
statistic	O
is	O
too	O
large	O
,	O
when	O
that	O
statistic	O
would	O
have	O
approximately	O
a	O
chi-square	O
distribution	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
In	O
minimum	B-General_Concept
chi-square	I-General_Concept
estimation	I-General_Concept
,	O
one	O
finds	O
the	O
values	O
of	O
parameters	O
that	O
make	O
that	O
test	O
statistic	O
as	O
small	O
as	O
possible	O
.	O
</s>
<s>
It	O
is	O
desired	O
to	O
test	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
population	O
from	O
which	O
this	O
sample	O
was	O
taken	O
follows	O
a	O
Poisson	O
distribution	O
.	O
</s>
<s>
One	O
could	O
apply	O
Pearson	B-General_Concept
's	I-General_Concept
chi-square	I-General_Concept
test	I-General_Concept
of	O
whether	O
the	O
population	O
distribution	O
is	O
a	O
Poisson	O
distribution	O
with	O
expected	O
value3.3	O
.	O
</s>
<s>
However	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
did	O
not	O
specify	O
that	O
it	O
was	O
that	O
particular	O
Poisson	O
distribution	O
,	O
but	O
only	O
that	O
it	O
is	O
some	O
Poisson	O
distribution	O
,	O
and	O
the	O
number	O
3.3	O
came	O
from	O
the	O
data	O
,	O
not	O
from	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
One	O
might	O
hope	O
that	O
the	O
resulting	O
test	O
statistic	O
would	O
have	O
approximately	O
a	O
chi-square	O
distribution	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
It	O
is	O
however	O
true	O
asymptotically	O
when	O
minimum	B-General_Concept
chi-square	I-General_Concept
estimation	I-General_Concept
is	O
used	O
.	O
</s>
<s>
Numerical	O
computation	O
shows	O
that	O
the	O
value	O
of	O
λ	O
that	O
minimizes	O
the	O
chi-square	B-General_Concept
statistic	I-General_Concept
is	O
about3.5242	O
.	O
</s>
<s>
For	O
that	O
value	O
of	O
λ	O
,	O
the	O
chi-square	B-General_Concept
statistic	I-General_Concept
is	O
about3.062764	O
.	O
</s>
<s>
If	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
had	O
specified	O
a	O
single	O
distribution	O
,	O
rather	O
than	O
requiring	O
λ	O
to	O
be	O
estimated	O
,	O
then	O
the	O
null	O
distribution	O
of	O
the	O
test	O
statistic	O
would	O
be	O
a	O
chi-square	O
distribution	O
with	O
10−1	O
=	O
9	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
Thus	O
the	O
observed	O
value	O
,	O
3.062764	O
,	O
is	O
quite	O
modest	O
,	O
and	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
rejected	O
.	O
</s>
