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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 鄭明燕 | |
| dc.contributor.author | Wei-Ying Wang | en |
| dc.contributor.author | 王惟穎 | zh_TW |
| dc.date.accessioned | 2021-06-13T03:37:59Z | - |
| dc.date.available | 2006-07-28 | |
| dc.date.copyright | 2006-07-28 | |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-07-27 | |
| dc.identifier.citation | [1] Berman, M. (1981). Inhomogeneous and modulated gamma processes.
Biometrika, 68, 143-152. [2] Berman, M. and Turner, T. R. (1992). Approximating point process likelihoods with GLIM. Applied Statistics, 41, 31-38. [3] Chen, Y.-I., Huang, C.-S. and Hong, C.-H. (2004). A statistical Assessment for the hazard of large aftershocks post to the Chi-Chi mainshok. TAO: Terrestrial, atmospheric, and oceanic sciences , 15, No.3, 493-502. [4] Chen, Y.-I., and Huang, C.-S. (2006). Time dependent b value for aftershock sequences. Preprint. [5] Cheng, M.-Y. (2006). Nonparametric modeling of nonhomogeneous Poisson processes. Preprint. [6] Choi, E. and Hall, P. (1999). Nonparametric approach to analysis of space- time data on earthquake occurrences. Journal of computational and graphical statistics, 8, 733-748. [7] Cowling, A., Hall, P., and Michael, J. P. (1996). Bootstrap confidence regions for the intensity of a Poisson point process. Journal of the American Statistical Association, 91, 1516-1524. [8] Cox, D. R. and Miller, H. D. (1965). The theory of stochastic processes. Lon- don: Methuen. [9] Cox, D. R. and Snell, E. J. (1968). A general definition of residuals. Journal of the Royal Statistical Society, Series B, 30, 248-275. [10] Diggle, P. (1985). A kernel method for smoothing point process data. Journal of the American Statistical Association, 34, 138-147. 18 [11] Diggle, P., and Marron, J. S. (1988). Equivalence of smoothing parameter se- lectors in density and intensity estimation. Journal of the American Statistical Association, 83, 793-800. [12] Estevez-Perez, G., Lorenzo-Cimadevila, H., and Quintela-Del-Rio, A. (2002). Nonparametric analysis of the time structure of seismicity in a geographic region. Annals of Geophysics, 45 (3-4), 497-511. [13] Gutenberg, R., and Richter C. F. (1944). Frequency of earthquakes in Califor- nia. Bulletin of the Seismological Society of America, 34, 185-188. [14] Hjort, N. L., and Jones, M. C. (1996). Locally parametric nonparametric den- sity estimation. The Annals of Statistics, 24, 1619-1647. [15] Loader, C. R. (1992). A log-linear model for a Poisson process change point. The Annals of Statistics, 20, 1391-1411. [16] Loader, C. R. (1996). Local likelihood density estimation. The Annals of Statistics, 24, 1602-1618. [17] Loader, C. R. (1999). Local likelihood and regression. Springer. [18] Ogata, Y. (1984). Transition from aftershock to normal activity: the 1965 rat islands earthquake aftershock sequence. Bulletin of the Seismological Society of America, 74, 1757-1765. [19] Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9-27. [20] Staniswalis, J. G. (1989) The kernel estimate of a regression function in likelihood-based models. Journal of the American Statistical Association, 84, 276-283. [21] Tibshirani, R., and Hastie, T. (1987). Local likelihood estimation. Journal of the American Statistical Association, 82, 559-567. [22] Utsu, T. (1961). Statistical study on the occurrence of aftershocks. The Geophysical Magazine, 30, 521-605. [23] Wiemer, S., and Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western US and Japan. Bulletin of the Seismological Society of America, 90, 859-869. [24] 洪千惠 (2004), 集集餘震風險之貝氏分析。國立中央大學統計研究所碩士論文。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/32232 | - |
| dc.description.abstract | 本文主要在估計非均勻地震資料的intensity函數，一般來說，這種資料被視為一非均勻的卜瓦松過程。我們使用Cheng (2006)所提出的local maximum likelihood 方法來估計，經由模擬出的地震資料，我們比較了此方法與有母數的最大概似估計法的差別，此外，我們也使用Ogata (1984)所提出的殘差診斷方法來檢驗這兩個估計法。最後，我們利用此方法來觀察台灣在1999年發生的集集大地震所引發的餘震序列。 | zh_TW |
| dc.description.abstract | This article considers estimating the
intensity of nonhomogeneous earthquake data, which can be modeled by a nonhomogeneous Poisson process. We use the local maximum likelihood method proposed by Cheng (2006) to estimate the intensity function. We compare our method with parametric MLE method through simulation. In addition, for examining each of the estimation method, we use a diagnosis tool of residual process proposed by Ogata (1984). With the local maximum likelihood estimator, we nvestigate the intensity of the aftershock sequence triggered by Chi-Chi earthquake, which occurred in Taiwan in 1999. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T03:37:59Z (GMT). No. of bitstreams: 1 ntu-95-R93221017-1.pdf: 1650253 bytes, checksum: d032a1d02e5b4a050fc6e0f8a24b00d0 (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | 1 Introduction 1
2 Local likelihood function 4 2.1 Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Local log-likelihood function . . . . . . . . . . . . . . . . . . . . . . 5 3 The simulation result 6 3.1 Data generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Residual process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 The data sets from intensity function lambda_1 . . . . . . . . . . . . . . . 7 3.4 The data sets from intensity function lambda_2 . . . . . . . . . . . . . . . 11 4 Chi-Chi aftershock sequence 14 4.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 The estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Conclusion and some remarks 17 Reference 18 ii | |
| dc.language.iso | en | |
| dc.subject | 模擬 | zh_TW |
| dc.subject | 地震 | zh_TW |
| dc.subject | 非均值卜松過程 | zh_TW |
| dc.subject | 局部概似函數 | zh_TW |
| dc.subject | 無母數方法 | zh_TW |
| dc.subject | nonhomogeneous Poisson process | en |
| dc.subject | simulation | en |
| dc.subject | nonparametric method | en |
| dc.subject | local likelihood | en |
| dc.subject | earthquake | en |
| dc.title | 非均勻地震資料的統計分析 | zh_TW |
| dc.title | Statistical Analysis of Nonhomogeneous Earthquake Data | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張淑惠,戴政,陳秀熙 | |
| dc.subject.keyword | 地震,非均值卜松過程,局部概似函數,無母數方法,模擬, | zh_TW |
| dc.subject.keyword | earthquake,nonhomogeneous Poisson process,local likelihood,nonparametric method,simulation, | en |
| dc.relation.page | 20 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2006-07-27 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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