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Kunstler Georges
traitcompet
Commits
c7f885b5
Commit
c7f885b5
authored
Sep 14, 2015
by
Kunstler Georges
Browse files
progress on CI of ratio with Fieller method
parent
e1cb0154
Changes
1
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Inline
Side-by-side
R/analysis/ratio.CI.R
View file @
c7f885b5
##
qt
(
p
=
0.025
,
df
=
100000
)
qnorm
(
0.025
)
library
(
MASS
)
...
...
@@ -29,7 +27,7 @@ mvrnorm <-
## define param
mean.v
<-
c
(
0.15
,
0.25
)
Sigma
<-
matrix
(
c
(
0.002
,
0.001
,
0.001
,
0.005
),
2
,
2
)
Sigma
<-
matrix
(
c
(
0.002
,
0.00
0
1
,
0.
0
001
,
0.005
),
2
,
2
)
# MC
res.mc
<-
mvrnorm
(
n
=
10000
,
mean.v
,
Sigma
)
ratio.mc
<-
res.mc
[,
1
]
/
res.mc
[,
2
]
...
...
@@ -38,21 +36,23 @@ hist(res.mc[,1], breaks = 100)
abline
(
v
=
quantile
(
res.mc
[,
1
],
probs
=
c
(
0.025
,
0.975
)))
hist
(
res.mc
[,
2
],
breaks
=
100
)
abline
(
v
=
quantile
(
res.mc
[,
2
],
probs
=
c
(
0.025
,
0.975
)))
hist
(
ratio.mc
,
breaks
=
1000
,
xlim
=
c
(
0
,
1.
4
))
hist
(
ratio.mc
,
breaks
=
1000
,
xlim
=
c
(
0
,
1.
5
))
abline
(
v
=
quantile
(
ratio.mc
,
probs
=
c
(
0.025
,
0.975
)))
abline
(
v
=
mean
(
res.mc
[,
1
])
/
mean
(
res.mc
[,
2
]),
col
=
'red'
)
## Fieller's theorem
# compute Ci of ratio based on Fieller's methods
ratio.ci
<-
function
(
mean.v
,
Sigma
,
alpha
=
0.05
){
ta
<-
-
qnorm
(
alpha
/
2
)
theta
<-
mean.v
[
1
]
/
mean.v
[
2
]
k
<-
ta
^
2
*
Sigma
[
2
,
2
]
/
(
theta
)
^
2
mm
<-
theta
+
(
k
/
(
1
-
k
))
*
(
theta
+
Sigma
[
1
,
2
]
/
Sigma
[
2
,
2
])
ci
<-
ta
/
(
mean.v
[
2
]
*
(
1
-
k
))
*
sqrt
(
Sigma
[
1
,
1
]
+2
*
theta
^
2
*
Sigma
[
2
,
2
]
-
k
*
(
Sigma
[
1
,
1
]
-
Sigma
[
1
,
2
]
^
2
/
Sigma
[
2
,
2
]))
return
(
c
(
q.l
=
mm
-
ci
,
q.h
=
mm
+
ci
))
}
##because lot of data approximate teh student by a normal
ta
<-
qnorm
(
0.025
)
g
<-
mean.v
[
1
]
*
mean.v
[
2
]
-
ta
^
2
*
Sigma
[
1
,
2
]
d
<-
mean.v
[
2
]
^
2
-
(
ta
*
Sigma
[
2
,
2
])
^
2
b
<-
mean.v
[
1
]
^
2
-
(
ta
*
Sigma
[
1
,
1
])
^
2
ci.b
<-
sqrt
(
g
^
2
-
d
*
b
)
abline
(
v
=
ratio.ci
(
mean.v
,
Sigma
),
col
=
'green'
)
q.l
<-
(
g
-
ci.b
)
/
d
q.h
<-
(
g
+
ci.b
)
/
d
abline
(
v
=
c
(
q.l
,
q.h
),
col
=
'green'
)
quantile
(
ratio.mc
,
probs
=
c
(
0.025
,
0.975
))
ratio.ci
(
mean.v
,
Sigma
)
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