Sample Size Estimation
3
Γ
3
4
Γ
5
5
Γ
5
π
Method
π
=
0
.
8
%
Ξ
π
=
0
.
5
%
Ξ
π
=
0
.
3
%
Ξ
10
L
o
g
N
I
ββ MLE [Iterations]
1.04281
0.93413
[
4
1
,
1
-
8
4
6
]
30.4
16.8
0.64944
0.64554
[
7
7
;
3
-
4
5
0
]
29.9
29.1
0.44185
0.42392
[
4
5
;
4
-
2
2
5
]
47.3
41.3
50
L
o
g
N
I
ββ MLE [Iterations]
0.86133
0.81255
[
3
4
;
1
-
3
4
8
]
7.7
1.6
0.57181
0.51608
[
4
4
;
1
4
-
1
3
1
]
14.4
3.2
0.35003
0.31199
[
2
4
;
1
1
-
5
9
]
16.7
4.0
100
L
o
g
N
I
ββ MLE [Iterations]
0.82731
0.80296
[
3
4
;
1
1
-
2
7
8
]
3.4
0.4
0.53740
0.50386
[
4
3
;
1
8
-
1
4
0
]
7.5
0.8
0.32444
0.30406
[
2
3
;
7
-
5
2
]
8.1
1.4
200
L
o
g
N
I
ββ MLE [Iterations]
0.81199
0.80078
[
3
4
;
2
1
-
1
3
9
]
1.5
0.1
0.52043
0.50151
[
4
3
;
1
9
-
1
0
1
]
4.1
0.3
0.30965
0.30096
[
2
3
;
1
2
-
4
2
]
3.2
0.3
500
L
o
g
N
I
ββ MLE [Iterations]
0.80535
0.80057
[
3
4
;
2
1
-
8
5
]
0.7
0.1
0.50774
0.50044
[
4
3
;
1
8
-
1
0
4
]
1.5
0.1
0.30326
0.30033
[
2
3
;
1
3
-
4
3
]
1.1
0.1
1000
L
o
g
N
I
ββ MLE [Iterations]
0.80081
0.80009
[
3
4
;
2
1
-
9
1
]
0.1 <0.05
0.50250
0.50007
[
4
2
;
2
2
-
8
5
]
0.5 <0.05
0.30128
0.30011
[
2
3
;
1
2
-
4
1
]
0.4 <0.05 2500
L
o
g
N
I
ββ MLE [Iterations]
0.80031
0.79999
[
3
4
;
2
1
-
7
9
]
<0.05 <0.01
0.50102
0.50003
[
4
3
;
1
9
-
1
1
2
]
0.2 <0.01
0.30022
0.29995
[
2
3
;
1
4
-
4
4
]
0.07 <0.05 5000
L
o
g
N
I
ββ MLE [Iterations]
0.80004
0.80000
[
3
4
;
2
1
-
7
6
]
<0.01 <0.01
0.50047
0.49999
[
4
3
;
1
9
-
9
3
]
0.1 <0.01
0.30007
0.29999
[
2
3
;
1
4
-
5
0
]
<0.05 <0.01 10000
L
o
g
N
I
ββ MLE [Iterations]
0.80003
0.79996
[
3
4
;
2
2
-
8
1
]
<0.01 <0.01
0.50008
0.49997
[
4
3
;
2
1
-
9
0
]
<0.05 <0.01
0.30003
0.29999
[
2
3
;
1
3
-
4
9
]
0.01 <0.01 50000
L
o
g
N
I
ββ MLE [Iterations]
0.79998
0.79998
[
3
4
;
2
1
-
6
4
]
<0.01 <0.01
0.50004
0.49998
[
4
2
;
2
1
-
1
1
4
]
<0.01 <0.01
0.30000
0.29999
[
2
3
;
1
2
-
4
7
]
0 <0.01 100000
L
o
g
N
I
ββ MLE [Iterations]
0.80000
0.80000
[
3
4
;
2
0
-
7
9
]
0 0
0.50000
0.49997
[
4
3
;
2
0
-
8
6
]
0 <0.01
0.30000
0.29999
[
2
3
;
1
3
-
3
9
]
0 <0.01