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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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Chi-square probability distribution : Contingency Table Chi-Square...

By: Sal Khan

Contingency Table Chi-Square Test

Making inferences based on sample data. Confidence intervals. Margin of error. Hypothesis testing.

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The Probability Distribution of Future Bad Debt Losses for a Given...

By: Haehling Von Lanzenauer, Christoph; Wright, Don D

Bibliography: leaves 17-18

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Probability and Theory of Errors

By: Woodward, Robert Simpson, 1849-1924

Errors, Theory of ; Probabilities

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Probability and theory of errors

By: Woodward, Robert Simpson, 1849-1924

Supplemental catalog subcollection information: Canadian Libraries Collection; Canadian University Library Collection; Candian History

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A Survey of Tables of Probability Distributions

By: Olkin, I.

Description: Journal of Research of the National Institute of Standards and Technology

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On Studying Relations Between Time Series in Climatology : Volume ...

By: V. Privalsky

Description: Space Dynamics Laboratory, Logan, Utah, USA. Relationships between time series are often studied on the basis of cross-correlation coefficients and regression equations. This approach is generally incorrect for time series, irrespective of the cross-correlation coefficient value, because relations between time series are frequency-dependent. Multivariate time series should be analyzed in both time and frequency domains, including fitting a parametric (p...

Bendat, J. and Piersol A.: Measurement and Analysis of Random Data, Wiley, New York, 1966.; Bendat, J. and Piersol, A.: Random Data, Analysis and Measurements Procedures, 2nd Edn., Wiley, New York, 1986.; Bendat, J. and Piersol, A.: Random Data, Analysis and Measurements Procedures, 4th Edn., Wiley, Hoboken, 2010.; Box, G. and Jenkins, G.: Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco, 1970.; Box, G., Jenkins, G., and Reinsel, G.: Time Series A...

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On Studying Relations Between Time Series in Climatology : Volume ...

By: V. Privalsky

Description: Space Dynamics Laboratory (ret.), Logan, Utah, USA. In climatology, relationships between time series are often studied on the basis of crosscorrelation coefficients and regression equations. This approach is generally incorrect for time series irrespective of the crosscorrelation coefficient value because relations between time series are frequency-dependent. Multivariate time series should be analyzed in both time and frequency domains, including...

Enfield, D., Mestas-Nunez, A., and Trimble, P.: The Atlantic Multidecadal Oscillation and its relationship to rainfall and river flows in the continental US, Geophys. Res. Lett., 28, 2077–2080, 2001.; Hannan, E. and Quinn, B.: The determination of the order of an autoregression, J. R. Stat. Soc., 41, 190–195, 1979.; Bendat, J. and Piersol, A.: Measurement and Analysis of Random Data, Wiley, New York, 1966.; Bendat, J. and Piersol, A.: Random Data, Analysis and Measuremen...

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Using Modern Time Series Analysis Techniques to Predict Enso Event...

By: M. Wimbush; J. I. Salisbury

Description: Echo Technology, PO. Box 527, Chepachet, RI, USA. We analyze the monthly 1866-2000 Southern Oscillation Index (SOI) data to determine:

1) whether the SOI data are sufficiently noise-free that useful predictions can be made from them, and

2) in particular, whether future ENSO events can be predicted from the SOI data. 

The "Hilbert-EMD" technique is used to aid the analysis. This new frequency-time algorithm...

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Similarity Estimators for Irregular and Age-uncertain Time Series ...

By: J. Kurths; K. Rehfeld

Description: Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not...

Babu, P. and Stoica, P.: Spectral analysis of nonuniformly sampled data – a review, Digit. Signal Process., 20, 359–378, doi:10.1016/j.dsp.2009.06.019, 2010.; Batyrshin, I., Sheremetov, L., and Velasco-Hernandez, J. X.: On axiomatic definition of time series shape association measures, in: Operations Research and Data Mining ORADM 2012 workshop proceedings, edited by: Villa-Vargas, U., Sheremetov, L., and Haasis, H....

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Similarity Estimators for Irregular and Age Uncertain Time Series ...

By: K. Rehfeld; J. Kurths

Description: Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, n...

Batyrshin, I., Sheremetov, L., and Velasco-Hernandez, J. X.: On axiomatic definition of time series shape association measures, in: Operations Research and Data Mining ORADM 2012 workshop proceedings, edited by: Villa-Vargas, U., Sheremetov, L., and Haasis, H.-D., National Polytechnic Institute, Mexico City, 1–12, 2012.; Berkelhammer, M., Sinha, A., Mudelsee, M., Cheng, H., Edwards, R. L., and Cannariato, K.: Persistent multidecadal power of the Indian Summer Monsoon, Ea...

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Improved Singular Spectrum Analysis for Time Series with Missing D...

By: F. Peng; B. Li; Y. Shen

Description: College of Surveying and Geo-informatics, Tongji University, Shanghai, China. Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution develops an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach is evaluated with...

Broomhead, D. S. and King, G. P.: Extracting qualitative dynamics from experimental data, Physica D, 20, 217–236, 1986.; Buchanan, P. A. and Ruhl, C. A.: Summary of suspended-solids concentration data, San Francisco Bay, California, water year 1998, Open File Report 99-189, US Geological Survey, San Francisco, 41 pp., 2000.; Buchanan, P. A. and Schoellhamer, D. H.: Summary of suspended solids concentration data, San Francisco Bay, California, water year 1997, Open File R...

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Plos One : Quantifying Memory in Complex Physiological Time- Serie...

By: Martin Gerbert Frasch

Description : In a time-series, memory is a statistical feature that lasts for a period of time and distinguishes the time-series from a random, or memory-less, process. In the present study, the concept of ‘‘memory length’’ was used to define the time period, or scale over which rare events within a physiological time-series do not appear randomly. The method is based on inverse statistical analysis and provides empiric evidence that rare fluctuations in cardio-respirat...

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Homogenising Time Series: Beliefs, Dogmas and Facts : Volume 6, Is...

By: P. Domonkos

Description: Centre for Climate Change (C3), Geography Dept., University Rovira i Virgili, Campus Terres de l'Ebre, C. Betánia 5, Tortosa, 43500, Spain. In the recent decades various homogenisation methods have been developed, but the real effects of their application on time series are still not known sufficiently. The ongoing COST action HOME (COST ES0601) is devoted to reveal the real impacts of homogenisation methods more detailed and with higher confidence than ...

Alexandersson, H.: A homogeneity test applied to precipitation data, J. Climatol., 6, 661–675, 1986.; Caussinus, H. and Mestre, O.: Detection and correction of artificial shifts in climate series, J. Roy. Stat. Soc. Series, C53, 405–425, 2004.; Domonkos, P.: Testing of homogenisation methods: purposes, tools and problems of implementation, Proceedings of the 5th Seminar and Quality Control in Climatological Databases, edited by: Lakatos, M., Szentimrey, T., Bihari, Z., a...

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Automated Classification of Persistent Scatterers Interferometry T...

By: S. Franceschini; A. Corsini; J. P. Iannacone; M. Berti

Description: Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di Bologna – Via Zamboni 67, 40127 Bologna, Italy. We present a new method for the automatic classification of Persistent Scatters Interferometry (PSI) time series based on a conditional sequence of statistical tests. Time series are classified into distinctive predefined target trends, such as uncorrelated, linear, quadratic, bilinear and discontinuous, that describe different style...

Draper, N. R. and Smith, H.: Applied regression analysis, John Wiley and Sons, New York, USA, 1981.; Davis, J. C.: Statistics and Data Analysis in Geology, John Wiley and Sons, New York, USA, 1986.; Ferretti, A., Prati, C., and Rocca, F.: Permanent scatterers in SAR interferometry, IEEE Trans. Geosci. Remote Sens., 39, 8–20, 2001.; Berardino, P., Fornaro, G., Lanari, R., and Sansosti, E.: A new algorithm for surface deformation monitoring based on small baseline differen...

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Automated Classification of Persistent Scatterers Interferometry T...

By: A. Corsini; S. Franceschini; J. P. Iannacone; M. Berti

Description: Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di Bologna, Via Zamboni 67, 40127 Bologna, Italy. We present a new method for the automatic classification of Persistent Scatters Interferometry (PSI) time series based on a conditional sequence of statistical tests. Time series are classified into distinctive predefined target trends (such as uncorrelated, linear, quadratic, bilinear and discontinuous) that describe different styles...

Berardino, P., Fornaro, G., Lanari, R., and Sansosti, E.: A new algorithm for surface deformation monitoring based on small baseline differential interferograms, IEEE Trans. Geosci. Rem. Sens., 40, 2375–2383, 2002.; Calabro, M. D., Schmidt, D. A. and Roering, J. J.: An examination of seasonal deformation at the Portuguese Bend landslide, southern California, using radar interferometry, J. Geophys. Res., 115, doi:10.1029/2009...

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Anthropogenic Radiative Forcing Time Series from Pre-industrial Ti...

By: M. M. Kvalevåg; R. B. Skeie; G. Myhre; K. Tanaka; T. K. Berntsen; C. R. Hoyle

Description: Center for International Climate and Environmental Research – Oslo (CICERO), Oslo, Norway. In order to use knowledge of past climate change to improve our understanding of the sensitivity of the climate system, detailed knowledge about the time development of radiative forcing (RF) of the earth atmosphere system is crucial. In this study, time series of anthropogenic forcing of climate from pre-industrial times until 2010, for all well established forci...

Albrecht, B. A.: Aerosols, cloud microphysics, and fractional cloudiness, Science, 245, 1227–1230, 1989.; Alpert, P., Kishcha, P., Kaufman, Y. J., and Schwarzbard, R.: Global dimming or local dimming?: Effect of urbanization on sunlight availability, Geophys. Res. Lett., 32, L17802, doi:10.1029/2005gl023320, 2005.; Bauer, S. E., Koch, D., Unger, N., Metzger, S. M., Shindell, D. T., and Streets, D. G.: Nitrate aerosols to...

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Evaluation of Satellite-derived Hcho Using Statistical Methods : V...

By: S. M. Kim; K. H. Baek; L. Wang; I. De Smedt; K. Chance; J. H. Kim; T. Kurosu; M. J. Newchurch

Description: Department of Atmospheric Science, Pusan National University, Korea. Most previous evaluations of satellite performance relied on pair wise comparisons with limited spatial and temporal coverage of surface-based measurements such as soundings and in-situ measurements. Especially, validation of satellite HCHO measurements is very difficult because ground-based HCHO measurements are extremely sparse. We use a new scientific approach, statistical analyses wit...

Abbot, D. S., Palmer, P. I., Martin, R. V., Chance, K. V., Jacob, D. J., and Guenther, A.: Seasonal and interannual variability of North American isoprene emissions as determined by formaldehyde column measurements from space, Geophys. Res. Lett., 30, 1886, doi:10.1029/2003GL017336, 2003.; Atkinson, R.: Atmospheric chemistry of VOCs and NOx, Atmos. Environ., 34, 2063–2101, 1352-2310/00, 2000.; Benning, L. and Wahner, A.: Measurements of atmospheric formaldehyd...

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Time Series Inversion of Spectra from Ground-based Radiometers : V...

By: P. Eriksson; O. M. Christensen

Description: Department of Earth and Space Sciences, Chalmers University of Technology, Gothenburg, Sweden. Retrieving time series of atmospheric constituents from ground-based spectrometers often requires different temporal averaging depending on the altitude region in focus. This can lead to several datasets existing for one instrument, which complicates validation and comparisons between instruments. This paper puts forth a possible solution by incorporating the ...

Askne, J. and Westwater, E.: A review of ground-based remote sensing of temperature and moisture by passive microwave radiometers, IEEE T. Geosci. Remote, GE-24, 340–352, 1986.; Baron, P., Ricaud, P., d. Noë, J. L., Eriksson, P., Merino, F., and Murtagh, D.: Studies for the Odin sub-millimetre radiometer: Retrieval methodology, Can. J. Phys., 80, 341–356, 2002.; Bleisch, R., Kämpfer, N., and Haefele, A.: Retrieval of tropospheric water vapour by using spectra of a 22 GHz...

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Time Series Inversion of Spectra from Ground-based Radiometers : V...

By: P. Eriksson; O. M. Christensen

Description: Department of Earth and Space Sciences, Chalmers University of Technology, Gothenburg, Sweden. Retrieving time series of atmospheric constituents from ground-based spectrometers often requires different temporal averaging depending on the altitude region in focus. This can lead to several datasets existing for one instrument which complicates validation and comparisons between instruments. This paper puts forth a possible solution by incorporating the t...

Askne, J. and Westwater, E.: A review of ground-based remote sensing of temperature and moisture by passive microwave radiometers, IEEE T. Geosci. Remote, 24, 340–352, 1986.; Baron, P., Ricaud, P., de La No{ë}, J., Eriksson, P., Merino, F., and Murtagh, D.: Studies for the Odin sub-millimetre radiometer: {R}etrieval methodology, Can. J. Phys., 80, 341–356, 2002.; Bleisch, R., Kämpfer, N., and Haefele, A.: Retrieval of tropospheric water vapour by using spectra of a 22 GH...

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Technical Note: Multispectral Lidar Time Series of Pine Canopy Chl...

By: T. Hakala; S. Kaasalainen; R. Mäkipää; O. Nevalainen

Description: Finnish Geospatial Research Institute (FGI), Masala, Finland. We present an empirical application of multispectral laser scanning for monitoring the seasonal and spatial changes in pine chlorophyll (a + b) content and upscaling the accurate leaf-level chlorophyll measurements into branch and tree level. The results show the capability of the new instrument for monitoring the changes in the shape and physiology of tree canopy: the spectral ...

Asner, G. P., Knapp, D. E., Kennedy-Bowdoin, T., Jones, M. O., Martin, R. E., Boardman, J., and Field, C. B: Carnegie Airborne Observatory: in-flight fusion of hyperspectral imaging and waveform light detection and ranging for three-dimensional studies of ecosystems, J. Appl. Remote Sens., 1, 013536, doi:10.1117/1.2794018, 2007.; Austin, A. T. and Ballaré, C. S.: Dual role of lignin in plant litter decomposition in terrestr...

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