Heavy-Line - GH Binroth · 43 50 Heavy-Line Guide rail GP...MC 2x45 ...
Heavy Rail Modeling
Transcript of Heavy Rail Modeling
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0 10000 20000 30000 40000 50000
0
1 0 0
3 0 0
5 0 0
vconf
Lag
A C F
0 200 400 600
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series : vconf
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0 1000 2000 3000 4000
0
2
4
6
8
1 0
Pareto
0 1000 2000 3000 4000
0 2 0 0 0
6 0 0 0
1 0
0 0 0
call holding
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000
0 . 6
0 . 7
0 . 8
0 . 9
1 . 0
1 . 1
1 . 2
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000
1
2
3
4
5
6
7
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number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000 5000
0 . 5
1 . 0
1 . 5
2 . 0
stable
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 2000 4000 6000 8000 10000
0 . 0
0 . 5
1 . 0
1 . 5
2 . 0
2 . 5
3 . 0
perturb
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 200 400 600 800
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
packet
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Hill plot
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000 5000
0 . 5
1 . 0
1 . 5
2 . 0
AltHill
theta
H i l l e s t i m a t e o f a l p h a
0.0 0.2 0.4 0.6 0.8 1.0
0 . 5
1 . 0
1 . 5
2 . 0
AltsmooHill
theta
H i l l e s t i m a t e o f a l p h a
0.0 0.2 0.4 0.6 0.8
1 . 0
1 . 4
1 . 8
2 . 2
AltHill and AltsmooHill
theta
H i l l e s t i m a t e o f a l p h a
0.0 0.2 0.4 0.6 0.8 1.0
0 . 5
1 . 0
1 . 5
2 . 0
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Hill plot
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 200 400 600 800
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
AltHill
theta
H i l l e s t i m a t e o f a l p h a
0.0 0.2 0.4 0.6 0.8 1.0
0 . 4
0 . 6
0 . 8
1 . 0
AltsmooHill
theta
H i l l e s t i m a t e o f a
l p h a
0.0 0.2 0.4 0.6 0.8 0 . 6
0 . 7
0 . 8
0 . 9 1
. 0
AltHill and AltsmooHill
theta
H i l l e s t i m a t e o f a
l p h a
0.0 0.2 0.4 0.6 0.8 1.0
0 . 4
0 . 6
0 . 8 1
. 0
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number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000
1
2
3
4
5
6
7
0 1000 2000 3000 4000
1 . 0
1 . 2
1 . 4
1 . 6
1 . 8
2 . 0
2 . 2
number of order statistics
q q - e s t i m a t e o f a l p h a
call holding times
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 200 400 600 800
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
0 200 400 600 800
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
number of order statistics
q q - e s t i m a t e o f a l p h a
packet interarrivals
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number of order statistics
M o m e n t e s t i m a t e o f g a m m a
0 200 400 600 800 1000
- 5
- 4
- 3
- 2
- 1
0
Moment
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 200 400 600 800 1000
0
1
2
3
4
5
6
Hill
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number of order statistics
M o m e n t e s t i m a t e o f g a m m a
0 1000 2000 3000 4000
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
call holding
number of order statistics
M o m e n t e s t i m a t e o f g a m m a
0 200 400 600 800
- 2
- 1
0
1
packet
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Lag
A C F
5 10 15 20
0 . 0
0 . 0
5
0 . 1
0
call holding
Lag
H e a v y T a i l e d A C F
5 10 15 20 25
0 . 0
0 . 0
5
0 . 1
0
call holding
Lag
A C F
5 10 15 20
0 . 0
0 . 0
2
0 . 0
4
0 . 0
6
packet
Lag
H e a v y T a i l e d A C F
5 10 15 20 25
0 . 0
0 . 0
2
0 . 0
4
0 . 0
6
packet
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Index
p a c f
2 4 6 8 10 12 14
- 1
. 0
- 0
. 5
0 .
0
0 .
5
1 .
0
AR(2)
lag
a i c
0 5 10 15
2 0 2 0 0
2 0 4 0 0
2 0 6 0 0
2 0 8 0 0
AIC, AR(2)
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number of coefficients
p h i
1 2 3 4 5
0 .
0
0 .
0 0 2
0 .
0 0 4
alpha=.969
number of coefficients
p h i
1 2 3 4 5
- 0
. 0 0 1
0 .
0
0 .
0 0 1
0 . 0
0 2
0 .
0 0 3
0 .
0 0 4
alpha=.8686
number of coefficients
p h i
1 2 3 4 5
- 0
. 0 0
1
0 .
0
0 .
0 0 1
0 .
0 0 2
0 .
0 0 3
0 . 0
0 4
alpha=.7189
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Hill plot
number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000 4000
0
1
2
3
4
AltHill
theta
H i l l e s t i m a t e o f a l p h a
0.2 0.4 0.6 0.8 1.0
1
2
3
4
AltsmooHill
theta
H i l l e s t i m a t e o f a l p h a
0.2 0.4 0.6 0.8 1 . 0
2 . 0
3 . 0
4 . 0
AltHill and AltsmooHill
theta
H i l l e s t i m a t e o f a l p h a
0.2 0.4 0.6 0.8 1.0
1
2
3
4
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quantiles of exponential
l o g s o r t e d d a t a
0 2 4 6 8
- 1 6
- 1 4
- 1 2
- 1 0
- 8
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quantiles of exponential
l o g s o r t e d d a t a
2 4 6 8
- 1 0 . 0
- 9 . 5
- 9 . 0
- 8 . 5
- 8 . 0
k=1500, alpha=3.52
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0 200400600800
0 . 4
0 . 6
0 . 8
1 . 0
1 . 2
1 . 4
order statistics
H i l l e s t i m a t e o f a l p h a f o r t h e r e
a l r e s i d u a l s
0 100 300 500
0 . 4
0 . 6
0 . 8
1 . 0
1 . 2
1 . 4
order statistics
H i l l e s t i m a t e o f a l p h a f o r t h e A R p r o c e s s
0 100 200 300 400
0 . 4
0 . 6
0 . 8
1 . 0
1 . 2
1 . 4
order statistics
H i l l e s t i m a t e o f a l p h a f o r Y u l e - W a l k e r
e s t i m a t e d r e s i d u a l s
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0 1000 2000 3000
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
isdn1
Lag
A C F
5 10 15 20
0 . 0
0 . 0
5
0 . 1
0
0 . 1
5idsn1
Lag
H e a v y T a i l e d A C F
5 10 15 20 25
0 . 0
0 . 0
5
0 . 1
0
0 . 1
5idsn1
Lag
P A C F
5 10 15 20 25
0 . 0
0 . 0
5
0 . 1
0
0 . 1
5
isdn1
Lag
H e a v y t a i l e d P A C F
5 10 15 20 25
0 . 0
0 . 0
5
0 . 1
0
0 . 1
5
isdn1
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number of order statistics
H i l l e s t i m a t e o f a l p h a
0 1000 2000 3000
0
1
2
3
4
5
Hill
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quantiles of exponential
l o g s o r t e d d a t a
2 4 6 8
0
2
4
number of coefficients
p h i
1 2 3 4 5 6
0 . 0
0 . 0
0 1
0 . 0
0 2
0 . 0
0 3
lag
a i c
0 5 10 15 20 25 30
1 4 6 8 0
1 4 7 0 0
1 4 7 2 0
1 4 7 4 0
1 4 7 6 0
AIC:isdn1
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number of coefficients
p h i
1 2 3 4 5 6
0
5 * 1 0 ^ - 1
7
1 0 ^ - 1
6
Independence of residuals
Lag
A C F
0 5 10 15 20 25 30
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series : isdn1col[1:1000]
Lag
A C F
0 5 10 15 20 25 30
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series : isdn1col[1000:2000]
Lag
A C F
0 5 10 15 20 25 30
0 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
Series : isdn1col[2000:3000]
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