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Peaks-over-threshold models

Peaks-over-threshold models. Szabolcs Erdélyi research assistant VITUKI Plc. Abstract. Used data POT model Choosing thresholds Results Summary. Used data. POT model. X 1 , X 2 , … independence, identically distributed random variables u high enough threshold

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Peaks-over-threshold models

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  1. Peaks-over-threshold models Szabolcs Erdélyi research assistant VITUKI Plc.

  2. Abstract • Used data • POT model • Choosing thresholds • Results • Summary

  3. Used data

  4. POT model X1 , X2 , … independence, identically distributed random variables u high enough threshold H(z) distribution function of GPD when y > 0, and

  5. POT model • Choosing threshold • Selecting data over threshold from daily maximum values • Declustering • Time of declustering (It’s necessary because of independence): 30-60 days • Calculate model parameters with maximum likelihood function • Representing results: return levels and confidence intervals with profile likelihood

  6. Choosing threshold Expected value of GPD, when threshold is u0: when < 1 (else infinity). Every u > u0: Expected value is linear, the shape parameter is constant function in u.

  7. 250 200 Átlagos meghaladás (cm) 150 100 y = -0.2844x + 289.2 50 100 200 300 400 500 600 700 800 900 Küszöbérték (cm) Average exceed curve Szeged(H)

  8. 1000 900 /s) 3 800 700 Átlagos meghaladás (m 600 y = -0.1741x + 970.2 500 400 0 500 1000 1500 2000 2500 3000 3 Küszöbérték (m /s) Average exceed curve Szeged(Q)

  9. 300 250 200 Átlagos meghaladás (cm) 150 100 y = -0.247x + 219.4 50 0 300 400 700 800 0 100 200 500 600 Küszöbérték (cm) Average exceed curve Polgár(H)

  10. 800 700 /s) 3 600 Átlagos meghaladás (m 500 400 y = -0.2677x + 1237.4 300 0 500 1000 1500 2000 2500 3000 3500 3 Küszöbérték (m /s) Average exceed curve Polgár(Q)

  11. Shape parameter

  12. Shape parameter

  13. Záhony(H)

  14. Záhony(H)

  15. Záhony(Q)

  16. Záhony(Q)

  17. Polgár(H)

  18. Polgár(Q)

  19. Results, Vásárosnamény

  20. Other results

  21. Summary • On the majotity of data series the fitting is appropriate, the results are resonable • The final result is slighty affected by the selection of thresholds • In the cause of the data of Polgár(Q) and Szolnok(Q) the model does not fit properly • The reason for that can be found in the incidental errors of the calculation of data

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