The Estimation of Probability of Extreme Events for Small Samples
Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pisarenko, V. F. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Pure and applied geophysics - Basel : Birkhäuser, 1939, 174(2017), 4 vom: 24. Feb., Seite 1547-1560 |
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| Übergeordnetes Werk: |
volume:174 ; year:2017 ; number:4 ; day:24 ; month:02 ; pages:1547-1560 |
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| DOI / URN: |
10.1007/s00024-017-1495-0 |
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| Katalog-ID: |
SPR000243248 |
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| 100 | 1 | |a Pisarenko, V. F. |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Estimation of Probability of Extreme Events for Small Samples |
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| 520 | |a Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. | ||
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| 650 | 4 | |a Seismic Moment |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Generalize Extreme Value |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Generalize Pareto Distribution |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Generalize Extreme Value Distribution |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Rodkin, M. V. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Pure and applied geophysics |d Basel : Birkhäuser, 1939 |g 174(2017), 4 vom: 24. Feb., Seite 1547-1560 |w (DE-627)265506743 |w (DE-600)1464028-4 |x 1420-9136 |7 nnns |
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10.1007/s00024-017-1495-0 doi (DE-627)SPR000243248 (SPR)s00024-017-1495-0-e DE-627 ger DE-627 rakwb eng Pisarenko, V. F. verfasserin aut The Estimation of Probability of Extreme Events for Small Samples 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 Rodkin, M. V. aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 174(2017), 4 vom: 24. Feb., Seite 1547-1560 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:174 year:2017 number:4 day:24 month:02 pages:1547-1560 https://dx.doi.org/10.1007/s00024-017-1495-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 174 2017 4 24 02 1547-1560 |
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10.1007/s00024-017-1495-0 doi (DE-627)SPR000243248 (SPR)s00024-017-1495-0-e DE-627 ger DE-627 rakwb eng Pisarenko, V. F. verfasserin aut The Estimation of Probability of Extreme Events for Small Samples 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 Rodkin, M. V. aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 174(2017), 4 vom: 24. Feb., Seite 1547-1560 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:174 year:2017 number:4 day:24 month:02 pages:1547-1560 https://dx.doi.org/10.1007/s00024-017-1495-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 174 2017 4 24 02 1547-1560 |
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10.1007/s00024-017-1495-0 doi (DE-627)SPR000243248 (SPR)s00024-017-1495-0-e DE-627 ger DE-627 rakwb eng Pisarenko, V. F. verfasserin aut The Estimation of Probability of Extreme Events for Small Samples 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 Rodkin, M. V. aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 174(2017), 4 vom: 24. Feb., Seite 1547-1560 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:174 year:2017 number:4 day:24 month:02 pages:1547-1560 https://dx.doi.org/10.1007/s00024-017-1495-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 174 2017 4 24 02 1547-1560 |
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10.1007/s00024-017-1495-0 doi (DE-627)SPR000243248 (SPR)s00024-017-1495-0-e DE-627 ger DE-627 rakwb eng Pisarenko, V. F. verfasserin aut The Estimation of Probability of Extreme Events for Small Samples 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 Rodkin, M. V. aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 174(2017), 4 vom: 24. Feb., Seite 1547-1560 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:174 year:2017 number:4 day:24 month:02 pages:1547-1560 https://dx.doi.org/10.1007/s00024-017-1495-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 174 2017 4 24 02 1547-1560 |
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10.1007/s00024-017-1495-0 doi (DE-627)SPR000243248 (SPR)s00024-017-1495-0-e DE-627 ger DE-627 rakwb eng Pisarenko, V. F. verfasserin aut The Estimation of Probability of Extreme Events for Small Samples 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing 2017 Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 Rodkin, M. V. aut Enthalten in Pure and applied geophysics Basel : Birkhäuser, 1939 174(2017), 4 vom: 24. Feb., Seite 1547-1560 (DE-627)265506743 (DE-600)1464028-4 1420-9136 nnns volume:174 year:2017 number:4 day:24 month:02 pages:1547-1560 https://dx.doi.org/10.1007/s00024-017-1495-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_381 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 174 2017 4 24 02 1547-1560 |
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| author |
Pisarenko, V. F. |
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Pisarenko, V. F. misc Statistical Moment misc Seismic Moment misc Generalize Extreme Value misc Generalize Pareto Distribution misc Generalize Extreme Value Distribution The Estimation of Probability of Extreme Events for Small Samples |
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The Estimation of Probability of Extreme Events for Small Samples Statistical Moment (dpeaa)DE-He213 Seismic Moment (dpeaa)DE-He213 Generalize Extreme Value (dpeaa)DE-He213 Generalize Pareto Distribution (dpeaa)DE-He213 Generalize Extreme Value Distribution (dpeaa)DE-He213 |
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The Estimation of Probability of Extreme Events for Small Samples |
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estimation of probability of extreme events for small samples |
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The Estimation of Probability of Extreme Events for Small Samples |
| abstract |
Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. © Springer International Publishing 2017 |
| abstractGer |
Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. © Springer International Publishing 2017 |
| abstract_unstemmed |
Abstract The most general approach to the study of rare extreme events is based on the extreme value theory. The fundamental General Extreme Value Distribution lies in the basis of this theory serving as the limit distribution for normalized maxima. It depends on three parameters. Usually the method of maximum likelihood (ML) is used for the estimation that possesses well-known optimal asymptotic properties. However, this method works efficiently only when sample size is large enough (~200–500), whereas in many applications the sample size does not exceed 50–100. For such sizes, the advantage of the ML method in efficiency is not guaranteed. We have found that for this situation the method of statistical moments (SM) works more efficiently over other methods. The details of the estimation for small samples are studied. The SM is applied to the study of extreme earthquakes in three large virtual seismic zones, representing the regime of seismicity in subduction zones, intracontinental regime of seismicity, and the regime in mid-ocean ridge zones. The 68%-confidence domains for pairs of parameter (ξ, σ) and (σ, μ) are derived. © Springer International Publishing 2017 |
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| title_short |
The Estimation of Probability of Extreme Events for Small Samples |
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https://dx.doi.org/10.1007/s00024-017-1495-0 |
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Rodkin, M. V. |
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10.1007/s00024-017-1495-0 |
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2024-07-03T14:53:10.231Z |
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| score |
7.3991566 |