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Mathematical Statistics (10,538 Books)


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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Plos One : Coffee Agroforests Remain Beneficial for Neotropical Bi...

By: Martin Krkosek

Description : Coffee agroforestry systems and secondary forests have been shown to support similar bird communities but comparing these habitat types are challenged by potential biases due to differences in detectability between habitats. Furthermore, seasonal dynamics may influence bird communities differently in different habitat types and therefore seasonal effects should be considered in comparisons. To address these issues, we incorporated seasonal effects and facto...

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SAT Math : SAT Prep: Test 1 Section 6 Part 2

By: Sal Khan

Problems 5-6 starting on page 408

Sal works through every problem in the first edition of the College Board Official SAT Study Guide (ISBN Number: 0-87447-718-2 published in 2004). You should take the practice tests on your own, grade them and then use these videos to understand the pro

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Compound, independent events : LeBron Asks: What are the chances o...

By: Sal Khan, LeBron James

LeBron James asks Sal how to determine the probability of making 10 free throws in a row

Introduction to probability. Independent and dependent events. Compound events. Mutual exclusive events. Addition rule for probability.

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Information Theory : Source Encoding

By: Brit Cruise

Introduction to coding theory!

The branches of mathematics that are involved in the study of the physical or biological or sociological world.

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Compound, independent events : LeBron Asks: What are the chances o...

By: Sal Khan, LeBron James

LeBron James asks Sal Khan if it is easier to make three free throws or one three-pointer.

Introduction to probability. Independent and dependent events. Compound events. Mutual exclusive events. Addition rule for probability.

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Ancient Cryptography : Frequency Stability

By: Brit Cruise

What is the difference between a coin flip and a blind guess?

The branches of mathematics that are involved in the study of the physical or biological or sociological world.

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Forecasting Age Specific Fertility Using Principal Components

By: James E. Hozik

Statistical Reference Document

Excerpt: Demographers traditionally have relied on the cohort-component method for calculating fertility projections; multiplying projected age-specific birth rates by the projected population of women in each age group to calculate a projected total number of births. Time series methods can also be used to do fertility projections. However, direct univariate or multivariate modeling of age-specific fertility rates requires working with about 36 time series, one each for...

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Convergence of Finite Multistep Predictors from Incorrect Models a...

By: David F. Findley

Statistical Reference Document

Excerpt: In a recent? paper [5], we described a generalization to univariate time series models of the hypothesis testing procedure of Vuong [l2] f or comparing incorrect statistical models for independent data. The focus of [5] was on model selection criteria related to one-step-ahead forecasting performance. We suggested there that when p-stepahead prediction is the goal, with p > 1, then different test statistics should be used for each choice of p. To identify approp...

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Design of Moving-Average Trend Filters Using Fidelity, Smoothness ...

By: Alistair Gray

Statistical Reference Document

Introduction: This report is concerned with the design of local trend estimation ? for non-seasonal time series using finite moving-averages. A particular objective is to try and improve current methods of trend estimation within seasonal adjustment procedures where nonseasonal trend ? play a key role, especially at the ends of series. For example, the seasonal adjustment procedure X-11 (see Shiskin et al. (1967)) uses trend ... originally developed by Henderson (1916) w...

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Exploring Bias in a Generalized Additive Model for Spatial Air Pol...

By: Richard T. Burnett

Government Reference Publication

Excerpt: During the past few years, the generalized additive model (GAM) has become a standard tool for epidemiologic analysis exploring the effect of air pollution on population health. Recently, the use of the GAM has been extended from time-series data to spatial data. Still more recently, it has been suggested that the use of GAMs to analyze time-series data results in air pollution risk estimates being biased upward and that concurvity in the time-series data result...

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Using Moving Total Mortality Counts to Obtain Improved Estimates f...

By: Steven Roberts

Government Reference Publication

Excerpt: In many cities of the United States, measurements of ambient particulate matter air pollution (PM) are available only once every 6 days. Time-series studies conducted in these cities that investigate the relationship between mortality and PM are restricted to using a single days PM as the measure of PM exposure. This is undesirable because current evidence suggests that the effects of PM on mortality are spread over multiple days. And studies have shown that usi...

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Crime and Justice in the United States and in England and Wales, 1...

By: Jan M. Chaiken

Excerpt: Whether measured by surveys of crime victims or by police statistics, serious crime rates are not generally higher in the United States than England. (All references to England include Wales.) According to 1995 victim surveys -- which measure robbery, assault, burglary, and motor vehicle theft -- crime rates are all higher in England than the United States (figures 1-4 of the report beginning on page 1). According to latest (1996) police statistics -- which meas...

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Content Domain Cognitive Domain Geometry Using Routine Procedures

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Statistics of Paleomagnetic Data

Physics Literature

Excerpt: The need for statistical analysis of paleomagnetic data has become apparent from the preceding chapters. For instance, we require a method for determining a mean direction from a set of observed directions. This method should provide some measure of uncertainty in the mean direction. Additionally, we need methods for testing the significance of field tests of paleomagnetic stability. Basic statistical methods for analysis of directional data are introduced in th...

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Does Eo Ndvi Seasonal Metrics Capture Variations in Species Compos...

By: P. Ceccato; S. Miehe; R. Fensholt; J. L. Olsen

Description: Center for Climate and Energy Economics, the Danish Energy Agency, Amaliegade 44, 1256 Copenhagen K, Denmark. Most regional scale studies of vegetation in the Sahel have been based on Earth observation (EO) imagery due to the limited number of sites providing continuous and long term in situ meteorological and vegetation measurements. From a long time series of coarse resolution normalized difference vegetation index (NDVI) data a greening of the Sahel s...

Anyamba, A. and Tucker, C. J.: Analysis of Sahelian vegetation dynamics using NOAA-AVHRR NDVI data from 1981–2003, J. Arid Environ., 63, 596–614, 2005.; Anyamba, A., Tucker, C. J., Huete, A. R., and Boken, K.: Monitoring Drought Using Coarse-Resolution Polar-Orbiting Satellite Data, in: Monitoring and Predicting Agricultural Drought: A Global Study, edited by: Boken, K., Cracknell, A., and Heathcote, R. L., New York, Oxford Univerisity Press, Oxford University Press, par...

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Global Assessment of Vegetation Index and Phenology Lab (Vip) and...

By: M. Marshall; E. Opiyo; Y. Kang; E. Okuto; M. Ahmed

Description: Climate Research Unit, World Agroforestry Centre, United Nations Ave, Gigiri, P.O. Box 30677, Nairobi, 00100, Kenya. Earth observation based long-term global vegetation index products are used by scientists from a wide range of disciplines concerned with global change. Inter-comparison studies are commonly performed to keep the user community informed on the consistency and accuracy of such records as they evolve. In this study, we compared two new ...

Asrar, G., Myneni, R. B., and Choudhury, B. J.: Spatial heterogeneity in vegetation canopies and remote sensing of absorbed photosynthetically active radiation: a modeling study, Remote Sens. Environ., 41, 85–103, 1992.; Baret, F., Weiss, M., Allard, D., Garrigues, S., Leroy, M., Jeanjean, H., Myneni, R., Privette, J., Morisette, J., Bohbot, H., Bosseno, R., Dedieu, G., Di Bella, C., Duchemin, B., Espana, M., Gond, V., Gu, X. F., Guyon, D., Lelong, C., Maisongrande, P., ...

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Characterizing Ecosystem-atmosphere Interactions from Short to Int...

By: H. Lange; N. Carvalhais; T. Grünwald; M. Reichstein; M. D. Mahecha; D. Papale; C. Bernhofer; G. Seufert

Description: Max-Planck-Institute for Biogeochemistry, Jena, Germany. Characterizing ecosystem-atmosphere interactions in terms of carbon and water exchange on different time scales is considered a major challenge in terrestrial biogeochemical cycle research. The respective time series are now partly comprising an observation period of one decade. In this study, we explored whether the observation period is already sufficient to detect cross relationships of the var...

Allen, M R. and Smith, L A.: Monte Carlo SSA: Detecting irregular oscillations in the presence of coloured noise, Journal of Climate, 9, 3373–3404, 1996.; Aubinet, M., Grelle, A., Ibrom, A., Rannik, Ü., Moncrieff, J., Foken, T., Kowalski, A S., Martin, P H., Berbigier, P., Bernhofer, C., Clement, R., Elbers, J., Granier, A., Grünwald, T., Morgenstern, K., Pilegaard, K., Rebmann, C., Snijders, W., Valentini, R., and Vesala, T.: Estimates of the annual net carbon and water...

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Natural Variability and Anthropogenic Effects in a Central Mediter...

By: G. Vivaldo; C. Taricco; M. Ghil; S. Alessio

Description: Dipartimento di Fisica Generale dell'Università, and Istituto di Fisica dello Spazio Interplanetario (IFSI–INAF), Torino, Italy. We evaluate the contribution of natural variability to the modern decrease in foraminiferal Δ18O by relying on a 2200-years-long, high-resolution record of oxygen isotopic ratio from a Central Mediterranean sediment core. Pre-industrial values are used to train and test two sets of algorithms that are able to forecas...

Bonino, G., Cini Castagnoli, G., Callegari, E., and Zhu, G. M.: Radiometric and tephroanalysis dating of recent Ionian sea cores, Nuovo Cimento C, 16, 155–161, 1993.; Box, G. and Jenkins, G.: Time series analysis: Forecasting and control, San Francisco, Holden-Day, 1970.; Childers, D. G.: Modern Spectrum Analysis, edited by: Childers, D. G., IEEE Press, New York, 1978; Cini Castagnoli, G., Bonino, G., Caprioglio, F., Provenzale, A., Serio, M., and Zhu, G. M.: The carbona...

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Verification Tools for Probabilistic Forecasts of Continuous Hydro...

By: F. Laio; S. Tamea

Description: Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Torino, Italy. In the present paper we describe some methods for verifying and evaluating probabilistic forecasts of hydrological variables. We propose an extension to continuous-valued variables of a verification method originated in the meteorological literature for the analysis of binary variables, and based on the use of a suitable cost-loss function to evaluate th...

Abramson, B. and Clemen, C.: Probability forecasting, Int. J. Forecast., 11, 1–4, 1995.; Berkovitz, J.: Testing density forecasts, with applications to risk management, J. Bus. Econ. Stat., 19, 465–474, 2001.; Beven, K.: A manifesto for the equifinality thesis, J. Hydrol., 320, 18–36, \doi10.1016/j.jhydrol.2005.07.007, 2006.; Box, G. E P. and Jenkins, G M.: Time series analysis: forecasting and control, Holden Day, San Francisco, CA, 1970.; Chatfield, C.: Prediction inte...

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Rainfall Nowcasting by at Site Stochastic Model P.R.A.I.S.E. : Vol...

By: D. L. De Luca; P. Versace; B. Sirangelo

Description: Dipartimento di Difesa del Suolo, Università della Calabria – Rende, Italy. The paper introduces a stochastic model to forecast rainfall heights at site: the P.R.A.I.S.E. model (Prediction of Rainfall Amount Inside Storm Events). PRAISE is based on the assumption that the rainfall height Hi+1 accumulated on an interval Δt between the instants iΔt and (i+1Δt is correlated with a variable Zi(Ν)

De Luca, D. L.: Metodi di previsione dei campi di pioggia. Tesi di Dottorato di Ricerca, Università della Calabria, Italy, 2005.; Abramowitz, M. and Stegun, I. A.: Handbook of mathematical functions, Dover, New York, NY, 1970.; Box, G. E. P. and Jenkins, G. M.: Time series analysis: forecasting and control, Holden-Day, S.Francisco, 1976.; Brockwell, P. J. and Davis, R. A.: Time Series. Theory and Methods, Springer Verlag, New York, NY, 1987.; Burlando, P., Rosso, R., Cad...

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