Examples for 11/18/2011
Fall 2011
X
1
, X
2
, … , X
n
Empirical Distribution Function:
S
(
x
)
=
[ number of
X
i
’s
that are
≤
x
]
/
n
H
0
:
X
1
, X
2
, … , X
n
are
i.i.d.
with
c.d.f.
F
(
x
)
Test Statistic
D
=
( ) ( )
F
S
sup
x
x
x

.
1.
Consider a data set:
34
62
70
15
77
94
50
42
132
85
100
28
55
66
120
50
112
20
8
145
Consider
H
0
:
X
1
, X
2
, … , X
17
are
i.i.d.
Gamma
with
α
= 5
and
θ
= 10.
S
(
x
)
=
[ number of
X
i
’s
that are
≤
x
]
/
n
=
[ number of
X
i
’s
that are
≤
x
]
/
20
☺
)/20
☺
= 1, 2, … , 20.
S
(
x
)
=
[ number of
X
i
’s
that are
<
x
]
/
n
=
[ number of
X
i
’s
that are
<
x
]
/
20
☺
)/20
☺
= 1, 2, … , 20.
If
T
has a Gamma
(
α
,
θ
=
1
/
λ
) distribution, where
α
is an integer, then
2
T
/
θ
=
2
λ
T
has a
χ
2
(
2
α
)
distribution
(
a chisquare distribution with
2
α
degrees of freedom
).
F
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 STEPHANOV
 Normal Distribution, Cumulative distribution function, GAMMA, Confidence band

Click to edit the document details