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

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Presentation on theme: "Peaks-over-threshold models Szabolcs Erdélyi research assistant VITUKI Plc."— Presentation transcript:

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

2 Abstract – Used data – POT model – Choosing thresholds – Results – Summary

3 Used data STATIONDATATYPEFROMTO TiszabecsH TivadarH TivadarQ VásárosnaményH VásárosnaményQ ZáhonyH ZáhonyQ PolgárH PolgárQ SzolnokH SzolnokQ SzegedH SzegedQ

4 POT model X 1, X 2, … independence, identically distributed random variables uhigh 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): 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 u 0 : when  u 0 : Expected value is linear, the shape parameter is constant function in u.

7 Average exceed curve Szeged(H)

8 Szeged(Q)

9 Polgár(H) y = x Küszöbérték (cm) Átlagos meghaladás (cm)

10 Average exceed curve Polgár(Q) y = x Küszöbérték (m 3 /s) Átlagos meghaladás (m 3 /s)

11 Shape parameter

12

13 Záhony(H)

14 Záhony(H)

15 Záhony(Q)

16 Záhony(Q)

17 Polgár(H)

18 Polgár(Q)

19 Results, Vásárosnamény DatatypeThreshold Scale parameter Shape parameter Return level in 100 years Confidence interval (95%) H300 cm cm[893, 944] H400 cm cm[893, 948] H500 cm cm[892, 946] H600 cm cm[889, 956] Q800 m 3 /s m 3 /s[3426, 4307] Q1100 m 3 /s m 3 /s[3427, 4395] Q1300 m 3 /s m 3 /s[3434, 4258] Q1500 m 3 /s m 3 /s[3441, 4253]

20 Other results StationDatatypeThreshold Return level in 100 years Confidence interval (95%) TiszabecsH300 cm679 cm[616, 864] TivadarH500 cm912 cm[875, 994] TivadarQ800 m 3 /s3188 m 3 /s[2692, 4680] ZáhonyH450 cm744 cm[718, 810] ZáhonyQ1500 m 3 /s3683 m 3 /s[3351, 4627] PolgárH470 cm789 cm[759, 871] SzolnokH600 cm949 cm[921, 1031] SzegedH550 cm937 cm[908, 1014] SzegedQ1500 m 3 /s4150 m 3 /s[3746, 5522]

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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