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Olle Eriksson
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     0       500           1000        1500   2000            2500     3000
x      y
   0    0.0
 300   -1.0
 600   -6.6
 710   -8.4
 840   -7.3
 950   -5.7
1070   -3.3
1300   -0.3
1600    0.0
1900   -1.6
2130   -1.3
2250   -1.8
2360   -2.1
2490   -3.8
2600   -5.7
2900   -7.9
3200    0.0
µ    sidol¨ge f¨r v¨nstersp˚
          a     o a          aret
σl   sp˚arbredd, l¨tta fordon
                   a
σt   sp˚arbredd, tunga fordon
τl   sp˚ararea, l¨tta fordon
                 a
τt   sp˚ararea, tunga fordon
f (xi, µ, σl , σt, τl , τt) =
                     2                               2
                                                        
           − 1 xi −µ                    1 xi −µ−1500
                                       −2
√ 1                                                          −τl
          e 2 σl         +√1           e       σl      
                                                               2 +
  2πσl                          2πσl

                   2                                    2
                                                        
            1 x −µ
           −2 i                             1 x −µ−2000
                                           −2 i σ
√ 1                                                          −τt
          e    σt
                         +√1           e           t      
                                                               2
  2πσt                          2πσt


V¨lj µ, σl , σt, τl , τt s˚ att
 a                        a
17
      (yi − f (xi, µ, σl , σt, τl , τt))2 minimeras
i=1
5
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5                                                                 q
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      0       500      1000         1500   2000          2500     3000
5
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      0       500           1000        1500   2000            2500   3000
V¨nster
        a        H¨ger
                  o
Tung    1790     6056
L¨tt
 a      1921     4317

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Session 76 Olle Eriksson

  • 2. q q q q q q q q q q q q q q q q q 0 500 1000 1500 2000 2500 3000
  • 3. q q q q 0 q q q q q −2 q q −4 q q −6 q q q q −8 0 500 1000 1500 2000 2500 3000
  • 4. q q q q 0 q q q q q −2 q q −4 q q −6 q q q q −8 0 500 1000 1500 2000 2500 3000
  • 5. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 6. 0 −2 −4 −6 −8 0 500 1000 1500 2000 2500 3000
  • 7. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 8. 0 −2 −4 −6 −8 0 500 1000 1500 2000 2500 3000
  • 9. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 10. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 11. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 12. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 13. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 14. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 15. q q q 0 q q q q q −2 q q q −4 q q −6 q q −8 q q 0 500 1000 1500 2000 2500 3000
  • 16. x y 0 0.0 300 -1.0 600 -6.6 710 -8.4 840 -7.3 950 -5.7 1070 -3.3 1300 -0.3 1600 0.0 1900 -1.6 2130 -1.3 2250 -1.8 2360 -2.1 2490 -3.8 2600 -5.7 2900 -7.9 3200 0.0
  • 17. µ sidol¨ge f¨r v¨nstersp˚ a o a aret σl sp˚arbredd, l¨tta fordon a σt sp˚arbredd, tunga fordon τl sp˚ararea, l¨tta fordon a τt sp˚ararea, tunga fordon
  • 18. f (xi, µ, σl , σt, τl , τt) = 2 2   − 1 xi −µ 1 xi −µ−1500 −2 √ 1 −τl e 2 σl +√1 e σl  2 + 2πσl 2πσl 2 2   1 x −µ −2 i 1 x −µ−2000 −2 i σ √ 1 −τt e σt +√1 e t  2 2πσt 2πσt V¨lj µ, σl , σt, τl , τt s˚ att a a 17 (yi − f (xi, µ, σl , σt, τl , τt))2 minimeras i=1
  • 19. 5 q q q q q q q 0 q q q q q q q q q q q q q q q q q q q q q q q q q −5 −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 20. 5 q q q 0 q q q q q q q q q q q q −5 q q −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 21. 5 q q 0 q q q q q −5 q q q q q q q q −10 q q −15 −20 0 500 1000 1500 2000 2500 3000
  • 22. 5 q q q q 0 q q q q q q q −5 q q q q q −10 q −15 −20 0 500 1000 1500 2000 2500 3000
  • 23. 5 q q q q q q q q q q q q q q 0 q q q q q q q q q q q q q q q q q q −5 −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 24. 5 q q 0 q q q q q q q q q q q q −5 q q q −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 25. 5 q q q q 0 q q q q q q q q q q q q q q q q q q q q q q q q q q q −5 −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 26. 5 q q 0 q q q q q q q q q q q q q q q −5 −10 −15 −20 0 500 1000 1500 2000 2500 3000
  • 27. V¨nster a H¨ger o Tung 1790 6056 L¨tt a 1921 4317