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Mathematical Statistics


Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. The term "mathematical statistics" is closely related to the term "statistical theory" but also embraces modelling for actuarial science and non-statistical probability theory, particularly in Scandinavia.

 
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Investigating the Earthquake Catalog of the National Observatory o...

By: G. Chouliaras

Description: National Observatory of Athens, Institute of Geodynamics, P.O. Box 20048, 11810 Athens, Greece. The earthquake catalog of the National Observatory of Athens (NOA) since the beginning of the Greek National Seismological Network development in 1964, is compiled and analyzed in this study. The b-value and the spatial and temporal variability of the magnitude of completeness of the catalog is determined together with the times of significant seismicity rate ...

Aki, K.: Maximum likelihood estimate of b in the formula log N{=}a – bM and its confidence limits, Bull. Earthq. Res. Inst. Tokyo Univ., 43, 237–239, 1965.; Bath, M.: The Seismology of Greece, Tectonophysics, 98, 165–208, 1983.; Bender, B.: Maximum likelihood estimation of b-values for magnitude grouped data, B. Seismol. Soc. Am., 73, 831–851, 1983.; Chouliaras, G.: Seismicity anomalies prior to the 8 June 2008, Mw{=}6.4 earthquake in Western Greece, Nat. Hazards Earth S...

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Investigating the Earthquake Catalog of the National Observatory o...

By: G. Chouliaras

Description: National Observatory of Athens, Institute of Geodynamics, P.O. Box 20048, 11810 Athens, Greece. The earthquake catalog of the National Observatory of Athens (NOA) since the beginning of the Greek National Seismological Network development in 1964, is compiled and analyzed in this study. The b-value and the spatial and temporal variability of the magnitude of completeness of the catalog is determined together with the times of significant seismicity rate ...

Aki, K.: Maximum likelihood estimate of b in the formula log N{=}a – bM and its confidence limits, Bull. Earthq. Res. Inst. Tokyo Univ., 43, 237–239, 1965.; Bath, M.: The Seismology of Greece, Tectonophysics, 98, 165–208, 1983.; Bender, B.: Maximum likelihood estimation of b-values for magnitude grouped data, B. Seismol. Soc. Am., 73, 831–851, 1983.; Chouliaras, G.: Seismicity anomalies prior to the 8 June 2008, Mw{=}6.4 earthquake in Western Greece, Nat. Hazards Earth S...

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Rogue Waves, Rogue Events and Extreme Wave Kinematics in Spatio-te...

By: A. Slunyaev; A. Sergeeva

Description: Institute of Applied Physics, Nizhny Novgorod, Russia. An approach to extensive studying rogue wave occurrence in numerical simulations is presented. As a result of numerical simulations of the unidirectional wave evolution, spatio-temporal fields of wave data of the size 20 min × 10 km are obtained with high resolution in time and space and are used for statistical analysis with the focus on extreme waves. Having the exhaustive information on the wave ...

Dommermuth, D. and Yue, D. K. P.: A high-order spectral method for the study of nonlinear gravity waves, J. Fluid Mech., 184, 267–288, 1987.; Annenkov, S. Y. and Shrira, V. I.: Evolution of kurtosis for wind waves, Geophys. Res. Lett., 36, L13603 doi:10.1029/2009GL038613, 2009.; Chalikov, D.: Statistical properties of nonlinear one-dimensional wave fields, Nonlin. Processes Geophys., 12, 671–689,

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Modeling Extreme Wave Heights from Laboratory Experiments with the...

By: M. Onorato; H. D. Zhang; C. Guedes Soares; Z. Cherneva

Description: Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Portugal. Spatial variation of nonlinear wave groups with different initial envelope shapes is theoretically studied first, confirming that the simplest nonlinear theoretical model is capable of describing the evolution of propagating wave packets in deep water. Moreover, three groups of laboratory experiments run in the wave basin of CEHIPA...

Alber, I. and Saffman, P.: Stability of random nonlinear deep-water waves with finite bandwidth spectra, Tech. Rep. 31326-6035-RU-00, TRW Defense and Space System Group, 1978.; Benjamin, T. B. and Feir, J. E.: The disintegration of wave trains on deep water. Part 1. Theory, J. Fluid Mech., 27, 417–430, 1967.; Bitner-Gregersen, E. M.: Nonlinear effects of the statistical model of shallow-water wind waves, Appl. Ocean Res., 2, 63–73, 1980.; Bitner-Gregersen, E. M. and Toff...

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Simplified Approach for Locating the Critical Probabilistic Slip S...

By: L. L. Liu; L. Li; Y. M. Cheng

Description: Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong. This paper aims to develop a rapid and practical procedure that can locate the slip surface for a slope with the minimum reliability index for limit equilibrium analysis at the minimum expense of time. The comparative study on the reliability indices from different sample numbers using the Monte Carlo Simulation Method has demonstrated that the results from la...

Arai, K. and Tagyo, K.: Determination of noncircular slip surfaces giving the minimum factor of safety in slope stability analysis, Soils Found., 21, 43–51, 1985.; Ang, A. H. and Tang, W.: Probability Concepts in Engineering Planning and Design, Vol. 2, John Wiley and Sons Inc., New York, 1984.; Au, S. K. and Beck, J. L.: Estimation of small failure probabilities in high dimensions by subset simulation, Probabilist Eng. Mech., 16, 263–277, 2001.; Au, S. K. and Beck, J. L...

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An Ising Model for Earthquake Dynamics : Volume 14, Issue 1 (19/01...

By: A. M. Posadas; A. Jiménez; K. F. Tiampo

Description: Department of Earth Sciences Biological and Geological Sciences, University of Western Ontario, London, Canada. This paper focuses on extracting the information contained in seismic space-time patterns and their dynamics. The Greek catalog recorded from 1901 to 1999 is analyzed. An Ising Cellular Automata representation technique is developed to reconstruct the history of these patterns. We find that there is strong correlation in the region, and that sm...

Aki, K.: Correlogram analyses of seismograms by means of a simple automatic computer, J. Phys. Earth, 4, 71–79, 1956.; Allègre, C J. and Le Mouel, J L.: Introduction of Scaling Technique in Brittle Failure of Rocks, Phys. Earth Planet Inter., 87, 85–93, 1994.; Allègre, C J., Le Mouel, J L., and Provost, A.: Scaling Rules in Rock Fracture and Possible Implications for Earthquake Predictions, Nature, 297, 47–49, 1982.; Anghel, M., Klein, W., Rundle, J B., and Martins, J S ...

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The Influence of Solar Wind Turbulence on Geomagnetic Activity : V...

By: Z. Vörös; J. Šimkanin; D. Jankovičovà

Description: Institute of Atmospheric Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic. The importance of space weather and its forecasting is growing as interest in studying geoeffective processes in the Sun – solar wind – magnetosphere – ionosphere coupled system is increasing. In this paper higher order statistical moments of interplanetary magnetic field and geomagnetic SYM-H index fluctuations are compared. The proper description of fl...

Baker, D. N., Pulkkinen, T. I., Angelopoulos, V., Baumjohann, W., and McPherron, R. L.: The neutral line model of substorms: Past results and present view, J. Geophys. Res., 101(A6), 12 975–13 010, 1996.; Balogh, A., Forsyth, R. J., Lucek, E. A., Horbury, T. S., and Smith, E. J.: Heliospheric magnetic field polarity inversions at high heliographic latitudes, Geophys. Res. Lett., 26, 631–634, 1999.; Bavassano, B., Woo, R., and Bruno, R.: Heliospheric plasma sheet and coro...

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Statistical Analysis of Transfer of Fluctuations in Solar Wind Tur...

By: W. M. MacEk; M. Strumik

Description: Space Research Centre, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warsaw, Poland. We present results of statistical analysis of the transfer of fluctuations in solar wind turbulence. We investigate the dynamics of the slow solar wind using an approach based on the Markov processes theory and experimental data measured by ACE spacecraft. In particular, we test whether the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cas...

Alexakis, A., Mininni, P D., and Pouquet, A.: Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence, Phys. Rev. E, 72, 046301, 2005.; Biskamp, D.: Magnetohydrodynamic Turbulence, Cambridge: University Press, 2003.; Bruno, R. and Carbone, V.: The Solar Wind as a Turbulence Laboratory, Living Reviews in Solar Physics, 2, 4, 2005.; Burlaga, L F.: Multifractal structure of the interplanetary magnetic field – Voyager 2 observations near 25 AU, 198...

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The Effect of Third-order Nonlinearity on Statistical Properties o...

By: E. M. Bitner-gregersen; M. Benoit; M. Onorato; A. Toffoli

Description: Det Norske Veritas, Veritasveien 1, Høvik, 1322, Norway. It is well established that third-order nonlinearity produces a strong deviation from Gaussian statistics in water of infinite depth, provided the wave field is long crested, narrow banded and sufficiently steep. A reduction of third-order effects is however expected when the wave energy is distributed on a wide range of directions. In water of arbitrary depth, on the other hand, third-order effec...

Ducrozet, G., Bonnefoy, F., Le Touzé, D., and Ferrant, P.: 3-D HOS simulations of extreme waves in open seas, Nat. Hazards Earth Syst. Sci., 7, 109–122, 2007.; Annenkov, S Y. and Shrira, V I.: Numerical modeling of water–wave evolution based on the Zakharov equation, J. Fluid. Mech., 449, 341–371, 2001.; Benjamin, T B.: Instability of periodic wave trains in nonlinear dispersive systems, Proc. Roy. Soc. London, A299, 59–75, 1967.; Clamond, D. and Grue, J.: A fast method ...

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Weighted Complex Networks Applied to Seismicity: the Itoiz Dam (No...

By: F. Luzón; A. Jiménez

Description: Department of Applied Physics, University of Almería, Carretera de Sacramento s/n, Cañada de San Urbano, 04120, Almería, Spain. On 18 September 2004, an earthquake of magnitude mbLg = 4.6 was recorded near the Itoiz dam (Northern Spain). It occurred after the first impoundment of the reservoir and has been catalogued by some authors as induced seismicity. We analyzed the seismicity in the region as weighted complex networks and tried to differentiate thi...

Båth, M.: Lateral inhomogeneities in the upper mantle, Tectonophysics, 2, 483–514, 1965.; Chen, S. and Chen, Q.: A weighted network model based on the preferential selection of edges, Appl. Math. Sci., 1(23), 1145–1156, 2007.; Barrat, A., Barthelemy, M., and Vespignani, A.: Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.; Abe, S. and Suzuki, N.: Small-world structure of earthquake network, Physica A, 337, 357–362, 2004a.; Abe, S. and...

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Evaluation of a Spectral Line Width for the Phillips Spectrum by M...

By: V. E. Zakharov; A. O. Korotkevich

Description: Department of Mathematics & Statistics, The University of New Mexico, MSC01 1115, 1 University of New Mexico, Albuquerque, NM 87131-0001, USA. The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the situations described by the Phillips spectrum. We evaluate a spectral line width of the spectrum from the simulations in the framework of primordial dyn...

Annenkov, S. Y. and Shrira, V. I.: Fast Nonlinear Evolution in Wave Turbulence, Phys. Rev. Lett., 102, 024502, doi:10.1103/PhysRevLett.102.024502, 2009.; Annenkov, S. Y. and Shrira, V. I.: Evolution of Wave Turbulence under Gusty Forcing, Phys. Rev. Lett., 107, 114502, doi:10.1103/PhysRevLett.107.114502, 2011.; Banner, M. L., Babanin, A. V., and Young...

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Polyphase Evolution of Pelagonia (Northern Greece) Revealed by Geo...

By: J.-p. Burg; M. G. Fellin; F. L. Schenker

Description: Department of Earth Sciences, ETH Zurich, Sonneggstrasse 5, 8092 Zurich, Switzerland. The Pelagonian zone, situated between the External Hellenides/Cyclades to the west and the Axios/Vardar/Almopias zone (AVAZ) and the Rhodope to the east, was involved in late Early Cretaceous and in Late Cretaceous–Eocene orogenic events whose duration and extent are still controversial. This paper constrains their late thermal imprints. New and previously published zir...

Baumgartner, P. O.: Jurassic sedimentary evolution and nappe emplacement in the Argolis Peninsula (Peloponnesus; Greece), Mém. Soc. Helv. Sci. Nat., 99, 1–111, 1985.; Anders, B., Reischmann, T., and Kostopoulos, D.: Zircon geochronology of basement rocks from the Pelagonian Zone, Greece: constraints on the pre-Alpine evolution of the westernmost Internal Hellenides, Internat. J. Earth Sci., 96, 639–661, 2007.; Aubouin, J.: Des tectoniques superposées et de leur significa...

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Dollars for Scholar Postsecondary Costs and Financing, 1990-1991

By: Rebecca Sutterlin

Statistical Reference Document

Excerpt: HIGHLIGHTS During school year 1990-1991 an estimated 20.6 (+.5) million high school graduates ages 17 or above were enrolled in postsecondary school for at least some time, approximately 14 (+.4) percent of that population. In 1990-1991 the average total costs of schooling for all postsecondary students, irrespective of type of school, level of enrollment, or amount of time spent in school, was $2,653 (+98) per student of the estimated 20.6 (+.5) million student...

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Paradoxist Distiches

By: Florentin Smarandache

The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues through these bi-verses closed in a new lyric exact formula, but with an opening to essence. For this kind of procedural poems one can elaborate mathematical algorithms and implement them in a computer: but, it...

I M M O D E S T With the shame Shamelessness U N D E C I D E D Fighting Himself J A Z Z ( I ) Melodious Anarchy J A Z Z ( I I ) Anarchic Melody

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World Health Organization Publication : Year 2003 ; Issue 92415803...

By: Derek Yach, Dr.

Medical Reference Publication

Summary High quality health statistics are essential for planning and implementing health policy in all country settings. In fact noncommunicable disease (NCD) risk factor data are crucial for predicting the future burden of chronic disease in populations and also for identifying potential interventions to reduce the future burden. The Surveillance of Risk Factors report (SuRF) presents, for the first time, country-level NCD risk factor prevalence data from the WHO Membe...

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Lead Exposure Associated

By: Environmental Protection Agency

Excerpt: Contributing Organizations This study was funded and managed by the U.S. Environmental Protection Agency. The study was conducted collaboratively by two organizations under contract to the Environmental Protection Agency, Battelle, and Midwest Research Institute. Each organization's responsibilities are listed below.

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Re-Engineering Rcra for Recycling Definition of Solid Waste Task F...

By: James R. Berlow

Excerpt: Although we received advice from many different individuals and groups from both inside and outside the Agency, these recommendations are our opinions and not necessarily those of EPA management or other staff. To reach our conclusions and recommendations, we worked very closely with the Association of State and Territorial Solid Waste Management Officials (ASTSWMO) and its Definition of Solid Waste Workgroup. We wish to thank everyone who helped us in this effo...

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Practical Regression and Anova Using R

By: Julian J. Faraway

Mathematics document containing theorems and formulas.

Excerpt: Before you start Statistics starts with a problem, continues with the collection of data, proceeds with the data analysis and finishes with conclusions. It is a common mistake of inexperienced Statisticians to plunge into a complex analysis without paying attention to what the objectives are or even whether the data are appropriate for the proposed analysis. Look before you leap! Formulation The formulation of a problem is often more essential than its solution ...

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A Guide to State Implementation of Icd-10 for Mortality Part II : ...

By: Department of Health and Human Services

Acknowledgments: This guide was prepared by Arialdi M. Minino of the Mortality Statistics Branch. Van L. Parsons of the Office of Research and Methodology and Jeffrey D. Maurer of the Mortality Statistics Branch contributed to the technical aspects of the guide. Harry M. Rosenberg, Robert N. Anderson, Kenneth D. Kochanek and Sherry L. Murphy of the Mortality Statistics Branch also contributed written material to the document.

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National Center for Health Statistics

By: Edward J. Sondik, Ph. D.

Overview: and Background. The National Center for Health Statistics (NCHS) is a unique public resource for health information. As the Nation’s principal health statistics agency, NCHS provides statistical information to guide actions and policies to improve the health of the American people. NCHS’s mission is to monitor America’s health, and our activities mirror the multi-faceted aspects of health care. NCHS surveys and data systems provide fundamental public health and...

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