References
- Antoniadis, A., A. Feuerverger, and P. Gonçalves. 2006. Wavelet-based estimation for univariate stable laws. Annals of the Institute of Statistical Mathematics 58 (4):779–807. doi:10.1007/s10463-006-0042-z.
- Beccar-Varela, M. P., H. Gonzalez-Huizar, M. C. Mariani, and O. K. Tweneboah. 2016. Use of wavelets techniques to discriminate between explosions and natural earthquakes. Physica A: Statistical Mechanics and Its Applications 457:42–51. doi:10.1016/j.physa.2016.03.077.
- Besbeas, P., and B. J. T. Morgan. 2008. Improved estimation of the stable laws. Statistics and Computing 18 (2):219–31. doi:10.1007/s11222-008-9050-6.
- Chong, K. H. 2019. Earthquake seismology I. https://www.ucl.ac.uk/EarthSci/people/lidunka/GEOL2014/Geophysics4%20-%20Seismic%20waves/Seismology/EARTHQUAKE%20SEISMOLOGY%20I.htm (accessed June 26, 2019).
- Dekkers, A. L., J. H. Einmahl, and L. De Haan. 1989. A moment estimator for the index of an extreme-value distribution. The Annals of Statistics 17 (4):1833–55. doi:10.1214/aos/1176347397.
- Donoho, D. L., and I. M. Johnstone. 1994. Ideal spatial adaptation via wavelet shrinkage. Biometrika 81 (3):425–55. doi:10.1093/biomet/81.3.425.
- Donoho, D. L., and I. M. Johnstone. 1995. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association 90 (432):1200–24. doi:10.1080/01621459.1995.10476626.
- Donoho, D. L., I. M. Johnstone, G. Kerkyacharian, and D. Picard. 1995. Wavelet shrinkage: Asymptopia? Journal of the Royal Statistical Society: Series B (Methodological) 57 (2):301–69. doi:10.1111/j.2517-6161.1995.tb02032.x.
- Fama, E., and R. Roll. 1971. Parameter estimates for symmetric stable distributions. Journal of the American Statistical Association 66 (334):331–38. doi:10.1080/01621459.1971.10482264.
- García Vargas, M., J. Rueda, R. M. García Blanco, and J. Mezcua. 2017. A real-time discrimination system of earthquakes and explosions for the mainland Spanish seismic network. Pure and Applied Geophysics 174 (1):213–28. doi:10.1007/s00024-016-1330-z.
- Gumbel, E. 1958. Statistics of extremes. New York: Columbia University Press.
- Hassannejad Bibalan, M., H. Amindavar, and M. Amirmazlaghani. 2017. Characteristic function based parameter estimation of skewed alpha-stable distribution: An analytical approach. Signal Processing 130:323–36. doi:10.1016/j.sigpro.2016.07.020.
- Hill, B. M. 1975. A simple general approach to inference about the tail of a distribution. The Annals of Statistics 3 (5):1163–74. doi:10.1214/aos/1176343247.
- Kahbasi, A., and A. Moradi. 2016. Earthquake-explosion discrimination using waveform cross-correlation technique for mines in southeast of Tehran. Journal of Seismology 20 (2):569–78. doi:10.1007/s10950-015-9544-6.
- Kateregga, M., S. Mataramvura, and D. Taylor. 2017. Parameter estimation for stable distributions with application to commodity futures log-returns. Cogent Economics and Finance 5 (1):1–28.
- Kongon, S. M., and D. B. Williams. 1998. Characteristic function based estimation of stable distribution parameters. In A practical guide to heavy tails: Statistical techniques and applications, ed R. J. Adler, R. E. Feldman, and M. Taqqu, 311–38. Cambridge: Birkhauser Boston Inc.
- Koutrouvelis, I. A. 1980. Regression-type estimation of the parameters of stable laws. Journal of the American Statistical Association 75 (372):918–28. doi:10.1080/01621459.1980.10477573.
- Kwang-Hyun, C. 2014. Discriminating between explosions and earthquakes. Applied Geophysics 11 (4):429–36.
- Linhares, R. R. 2016. Smoothed detrended fluctuation analysis. Journal of Statistical Computation and Simulation 86 (17):3388–97.
- McCulloch, J. H. 1997. Measuring tail thickness to estimate the stable index alpha. Journal of Business and Economic Statistics 15:74–81.
- Mohammadi, M., and A. Mohammadpour. 2014. Estimating the parameters of an á-stable distribution using the existence of moments of order statistics. Statistics & Probability Letters 90:78–84. doi:10.1016/j.spl.2014.03.008.
- Nolan, J. P. 1999. Stable Distributions. Washington, DC: University of Washington. Preprint.
- Nolan, J. P. 2001. Maximum likelihood estimation of stable parameters. In Lévy processes: Theory and applications, ed. O. E. Barndorff-Nielsen, T. Mikosch, and S. I. Resnick, 379–400. Boston: Birkhäuser.
- Press, S. J. 1972. Estimation in univariate and multivariate stable distributions. Journal of the American Statistical Association 67 (340):842–46. doi:10.1080/01621459.1972.10481302.
- Resnick, S., and C. Stărică. 1997. Smooth the hill estimator. Advances in Applied Probability 29 (1):271–93. doi:10.2307/1427870.
- Rohatgi, V. K. 1976. An Introduction to Probability Theory and Mathematical Statistics. New York: John Wiley and Sons.
- Shokripour, M., and M. Aminghafari. 2015. Wavelet-based estimation for multivariate stable laws. Journal of Statistical Computation and Simulation 85 (8):1584–600. doi:10.1080/00949655.2014.881815.
- Vidakovic, B. 1999. Statistical Modeling by Wavelets. New York: Wiley.
- Zolotarev, V. 1986. One-Dimensional Stable Distributions. Providence, RI: American Mathematical Society.