Envstats

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EnvStats

Author : Steven P. Millard
Publisher : Springer Science & Business Media
ISBN 13 : 1461484561
Total Pages : 291 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis EnvStats by : Steven P. Millard

Download or read book EnvStats written by Steven P. Millard and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes EnvStats, a new comprehensive R package for environmental statistics and the successor to the S-PLUS module EnvironmentalStats for S-PLUS (first released in 1997). EnvStats and R provide an open-source set of powerful functions for performing graphical and statistical analyses of environmental data, bringing major environmental statistical methods found in the literature and regulatory guidance documents into one statistical package, along with an extensive hypertext help system that explains what these methods do, how to use these methods, and where to find them in the environmental statistics literature. EnvStats also includes numerous built-in data sets from regulatory guidance documents and the environmental statistics literature. This book shows how to use EnvStats and R to easily: * graphically display environmental data * plot probability distributions * estimate distribution parameters and construct confidence intervals on the original scale for commonly used distributions such as the lognormal and gamma, as well as do this nonparametrically * estimate and construct confidence intervals for distribution percentiles or do this nonparametrically (e.g., to compare to an environmental protection standard) * perform and plot the results of goodness-of-fit tests * compute optimal Box-Cox data transformations * compute prediction limits and simultaneous prediction limits (e.g., to assess compliance at multiple sites for multiple constituents) * perform nonparametric estimation and test for seasonal trend (even in the presence of correlated observations) * perform power and sample size computations and create companion plots for sampling designs based on confidence intervals, hypothesis tests, prediction intervals, and tolerance intervals * deal with non-detect (censored) data * perform Monte Carlo simulation and probabilistic risk assessment * reproduce specific examples in EPA guidance documents EnvStats combined with other R packages (e.g., for spatial analysis) provides the environmental scientist, statistician, researcher, and technician with tools to “get the job done!”

Statistical Methods in Water Resources

Author : D.R. Helsel
Publisher : Elsevier
ISBN 13 : 9780080875088
Total Pages : 546 pages
Book Rating : 4.8/5 (75 download)

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Book Synopsis Statistical Methods in Water Resources by : D.R. Helsel

Download or read book Statistical Methods in Water Resources written by D.R. Helsel and published by Elsevier. This book was released on 1993-03-03 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data on water quality and other environmental issues are being collected at an ever-increasing rate. In the past, however, the techniques used by scientists to interpret this data have not progressed as quickly. This is a book of modern statistical methods for analysis of practical problems in water quality and water resources. The last fifteen years have seen major advances in the fields of exploratory data analysis (EDA) and robust statistical methods. The 'real-life' characteristics of environmental data tend to drive analysis towards the use of these methods. These advances are presented in a practical and relevant format. Alternate methods are compared, highlighting the strengths and weaknesses of each as applied to environmental data. Techniques for trend analysis and dealing with water below the detection limit are topics covered, which are of great interest to consultants in water-quality and hydrology, scientists in state, provincial and federal water resources, and geological survey agencies. The practising water resources scientist will find the worked examples using actual field data from case studies of environmental problems, of real value. Exercises at the end of each chapter enable the mechanics of the methodological process to be fully understood, with data sets included on diskette for easy use. The result is a book that is both up-to-date and immediately relevant to ongoing work in the environmental and water sciences.

Modern Statistics with R

Author : Måns Thulin
Publisher : BoD - Books on Demand
ISBN 13 : 9152701514
Total Pages : 598 pages
Book Rating : 4.1/5 (527 download)

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Book Synopsis Modern Statistics with R by : Måns Thulin

Download or read book Modern Statistics with R written by Måns Thulin and published by BoD - Books on Demand. This book was released on 2021-07-28 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decades have transformed the world of statistical data analysis, with new methods, new types of data, and new computational tools. The aim of Modern Statistics with R is to introduce you to key parts of the modern statistical toolkit. It teaches you: - Data wrangling - importing, formatting, reshaping, merging, and filtering data in R. - Exploratory data analysis - using visualisation and multivariate techniques to explore datasets. - Statistical inference - modern methods for testing hypotheses and computing confidence intervals. - Predictive modelling - regression models and machine learning methods for prediction, classification, and forecasting. - Simulation - using simulation techniques for sample size computations and evaluations of statistical methods. - Ethics in statistics - ethical issues and good statistical practice. - R programming - writing code that is fast, readable, and free from bugs. Starting from the very basics, Modern Statistics with R helps you learn R by working with R. Topics covered range from plotting data and writing simple R code to using cross-validation for evaluating complex predictive models and using simulation for sample size determination. The book includes more than 200 exercises with fully worked solutions. Some familiarity with basic statistical concepts, such as linear regression, is assumed. No previous programming experience is needed.

Statistics for Environmental Science and Management

Author : Bryan F.J. Manly
Publisher : CRC Press
ISBN 13 : 1439878129
Total Pages : 312 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Statistics for Environmental Science and Management by : Bryan F.J. Manly

Download or read book Statistics for Environmental Science and Management written by Bryan F.J. Manly and published by CRC Press. This book was released on 2008-10-21 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a nonmathematical approach to this topic, Statistics for Environmental Science and Management introduces frequently used statistical methods and practical applications for the environmental field. This second edition features updated references and examples along with new and expanded material on data quality objectives, the generalized linear model, spatial data analysis, and Monte Carlo risk assessment. Additional topics covered include environmental monitoring, impact assessment, censored data, environmental sampling, the role of statistics in environmental science, assessing site reclamation, and drawing conclusions from data.

EnvironmentalStats for S-Plus

Author : Steven P. Millard
Publisher : Springer Science & Business Media
ISBN 13 : 1468404601
Total Pages : 386 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis EnvironmentalStats for S-Plus by : Steven P. Millard

Download or read book EnvironmentalStats for S-Plus written by Steven P. Millard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENVIRONMENTALSTATS for S-PLUS, a new add-on module to S-PLUS, is the first comprehensive software package for environmental scientists, engineers, and regulators. ENVIRONMENTALSTATS for S-PLUS provides a set of powerful yet simple-to-use functions for performing graphical and statistical analyses of environmental data, including parameter and quantile estimation, methods for dealing with non-detects, power and sample size calculations, prediction and tolerance intervals, and probabilistic risk assessment. ENVIRONMENTALSTATS for S-PLUS includes an extensive hyptertext help system that explains methods from the environmental literature and regulatory guidance documents, along with a glossary of commonly used statistical and environmental terms. This users manual provides the documentation for Versions 1.0 and 1.1 of the ENVIRONMENTALSTATS for S-PLUS module. Version 1.0 works under S-PLUS 3.3/3.4 and Version 1.1 works under S-PLUS 4.0.

Statistics for Censored Environmental Data Using Minitab and R

Author : Dennis R. Helsel
Publisher : John Wiley & Sons
ISBN 13 : 0470479884
Total Pages : 344 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Statistics for Censored Environmental Data Using Minitab and R by : Dennis R. Helsel

Download or read book Statistics for Censored Environmental Data Using Minitab and R written by Dennis R. Helsel and published by John Wiley & Sons. This book was released on 2012-02-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition " . . . an excellent addition to an upper-level undergraduate course on environmental statistics, and . . . a 'must-have' desk reference for environmental practitioners dealing with censored datasets." —Vadose Zone Journal Statistics for Censored Environmental Data Using Minitab® and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates well-established methods from other disciplines into new solutions for environmental studies. This new edition applies methods of survival analysis, including methods for interval-censored data to the interpretation of low-level contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab® into the discussed analyses, the book features newly developed and updated material including: A new chapter on multivariate methods for censored data Use of interval-censored methods for treating true nondetects as lower than and separate from values between the detection and quantitation limits ("remarked data") A section on summing data with nondetects A newly written introduction that discusses invasive data, showing why substitution methods fail Expanded coverage of graphical methods for censored data The author writes in a style that focuses on applications rather than derivations, with chapters organized by key objectives such as computing intervals, comparing groups, and correlation. Examples accompany each procedure, utilizing real-world data that can be analyzed using the Minitab® and R software macros available on the book's related website, and extensive references direct readers to authoritative literature from the environmental sciences. Statistics for Censored Environmental Data Using Minitab® and R, Second Edition is an excellent book for courses on environmental statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for??environmental professionals, biologists, and ecologists who focus on the water sciences, air quality, and soil science.

Municipal Solid Waste Management in Asia and the Pacific Islands

Author : Agamuthu Pariatamby
Publisher : Springer Science & Business Media
ISBN 13 : 9814451738
Total Pages : 377 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Municipal Solid Waste Management in Asia and the Pacific Islands by : Agamuthu Pariatamby

Download or read book Municipal Solid Waste Management in Asia and the Pacific Islands written by Agamuthu Pariatamby and published by Springer Science & Business Media. This book was released on 2013-09-05 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid waste management issues, technologies and challenges are dynamic. More so, in developing and transitory nations in Asia. This book, written by Asian experts in solid waste management, explores the current situation in Asian countries including Pacific Islands. There are not many technical books of this kind, especially dedicated to this region of the world. The chapters form a comprehensive, coherent investigation in municipal solid waste (MSW) management, including, definitions used, generation, sustainable waste management system, legal framework and impacts on global warming. Several case studies from Asian nations are included to exemplify the real situation experienced. Discussions on MSW policy in these countries and their impacts on waste management and minimization (if any) are indeed an eye-opener. Undoubtedly, this book would be a pioneer in revealing the latest situation in the Asian region, which includes two of the world’s most dynamic nations in the economic growth. It is greatly envisaged to form an excellent source of reference in MSW management in Asia and Pacific Islands. This book will bridge the wide gap in available information between the developed and transitory/developing nations.

Lake Victoria Fisheries Resources

Author : Yunus D. Mgaya
Publisher : Springer
ISBN 13 : 3319696564
Total Pages : 287 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Lake Victoria Fisheries Resources by : Yunus D. Mgaya

Download or read book Lake Victoria Fisheries Resources written by Yunus D. Mgaya and published by Springer. This book was released on 2017-11-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book synthesises the historical trends of the lake fisheries, the lake ecology, biology and biodiversity, socio-economics, stock assessment, aquaculture, fish quality assurance, environmental quality and management of the fisheries resources. The evolution of fisheries in Lake Victoria has undergone dramatic changes over the last few decades, leading to both ecological and socio-economic consequences. The lake has changed from one dominated by haplochromines in the 1950s, to one currently dominated by Nile perch, ‘dagaa’ (Rastrineobola argentea) and Nile tilapia. These changes have mainly been driven by the introduction of the predatory Nile perch in the lake, eutrophication due to increased human activities in the catchment, increased human population growth, overfishing and changes in the global climate system. This work should therefore be a particularly useful reference to fisheries scientists and managers, potential investors, students and other professionals who may be interested in the Lake Victoria fisheries.

Nonparametric and Semiparametric Models

Author : Wolfgang Karl Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 364217146X
Total Pages : 300 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Nonparametric and Semiparametric Models by : Wolfgang Karl Härdle

Download or read book Nonparametric and Semiparametric Models written by Wolfgang Karl Härdle and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

An Introduction to Statistical Concepts

Author : Debbie L. Hahs-Vaughn
Publisher : Routledge
ISBN 13 : 1317228731
Total Pages : 1187 pages
Book Rating : 4.3/5 (172 download)

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Book Synopsis An Introduction to Statistical Concepts by : Debbie L. Hahs-Vaughn

Download or read book An Introduction to Statistical Concepts written by Debbie L. Hahs-Vaughn and published by Routledge. This book was released on 2020-02-03 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of An Introduction to Statistical Concepts is designed to help students really understand statistical concepts, the situations in which they can be used, and how to apply them to data. Hahs-Vaughn and Lomax discuss the most popular, along with many of the lesser-known, procedures and models, whilst also exploring nonparametric procedures used when standard assumptions are violated. They provide in-depth coverage of testing assumptions and highlight several online tools for computing statistics (e.g., effect sizes and their confidence intervals and power). This comprehensive, flexible, and accessible text includes a new chapter on mediation and moderation; expanded coverage of effect sizes; and discussions of sensitivity, specificity, false positive, and false negative, along with using the receiver operator characteristic (ROC) curve. In addition to instructions and screen shots for using SPSS, new to this edition is annotated script for using R. This book, noted for its crystal-clear explanations, and its inclusion of only the most crucial equations, is an invaluable resource for students undertaking a course in statistics in any number of social science and behavioral disciplines—from education, business, communication, exercise science, psychology, sociology and more.

Statistical Analysis with R For Dummies

Author : Joseph Schmuller
Publisher : John Wiley & Sons
ISBN 13 : 1119337267
Total Pages : 456 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Statistical Analysis with R For Dummies by : Joseph Schmuller

Download or read book Statistical Analysis with R For Dummies written by Joseph Schmuller and published by John Wiley & Sons. This book was released on 2017-03-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures. But now, thanks to Statistical Analysis with R For Dummies, you have access to a trusted, easy-to-follow guide that focuses on the foundational statistical concepts that R addresses—as well as step-by-step guidance that shows you exactly how to implement them using R programming. People are becoming more aware of R every day as major institutions are adopting it as a standard. Part of its appeal is that it's a free tool that's taking the place of costly statistical software packages that sometimes take an inordinate amount of time to learn. Plus, R enables a user to carry out complex statistical analyses by simply entering a few commands, making sophisticated analyses available and understandable to a wide audience. Statistical Analysis with R For Dummies enables you to perform these analyses and to fully understand their implications and results. Gets you up to speed on the #1 analytics/data science software tool Demonstrates how to easily find, download, and use cutting-edge community-reviewed methods in statistics and predictive modeling Shows you how R offers intel from leading researchers in data science, free of charge Provides information on using R Studio to work with R Get ready to use R to crunch and analyze your data—the fast and easy way!

Solid Waste Management in Nepal

Author : Asian Development Bank
Publisher : Asian Development Bank
ISBN 13 : 9292542338
Total Pages : 135 pages
Book Rating : 4.2/5 (925 download)

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Book Synopsis Solid Waste Management in Nepal by : Asian Development Bank

Download or read book Solid Waste Management in Nepal written by Asian Development Bank and published by Asian Development Bank. This book was released on 2013-08-01 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Managing solid waste is one of the major challenges in urbanization. A survey conducted in all 58 municipalities of Nepal in 2012 found that the average municipal solid waste generation was 317 grams per capita per day. This translates into 1,435 tons per day or 524,000 tons per year of municipal solid waste generation in Nepal. Many of these technically and financially constrained municipalities are still practicing roadside waste pickup from open piles and open dumping, creating major health risks.

Environmental Statistics with S-PLUS

Author : Steven P. Millard
Publisher : CRC Press
ISBN 13 : 142003717X
Total Pages : 848 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Environmental Statistics with S-PLUS by : Steven P. Millard

Download or read book Environmental Statistics with S-PLUS written by Steven P. Millard and published by CRC Press. This book was released on 2000-09-21 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, comprehensive treatment of the subject, Environmental Statistics with S-PLUS surveys the vast array of statistical methods used to collect and analyze environmental data. The book explains what these methods are, how to use them, and where to find references to them. In addition, it provides insight into what to think about before you collect environmental data, how to collect the data, and how to make sense of it after collection. A unique and powerful feature of the book is its integration with the commercially available software package S-Plus and the add-on modules EnvironmentalStats for S-PLUS, S+SpatialStats, and S-PLUS for ArcView. The book presents data sets to explain statistical methods, and then shows how to implement these methods by providing the commands for and the results from the software. This survey of statistical methods, definitions, and concepts helps you collect and effectively analyze data for environmental pollution problems. Using the S-PLUS software in conjunction with this text will no doubt increase understanding of the methods.

Statistical Analysis with R For Dummies

Author : Joseph Schmuller
Publisher : John Wiley & Sons
ISBN 13 : 1119337062
Total Pages : 467 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Statistical Analysis with R For Dummies by : Joseph Schmuller

Download or read book Statistical Analysis with R For Dummies written by Joseph Schmuller and published by John Wiley & Sons. This book was released on 2017-03-20 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures. But now, thanks to Statistical Analysis with R For Dummies, you have access to a trusted, easy-to-follow guide that focuses on the foundational statistical concepts that R addresses—as well as step-by-step guidance that shows you exactly how to implement them using R programming. People are becoming more aware of R every day as major institutions are adopting it as a standard. Part of its appeal is that it's a free tool that's taking the place of costly statistical software packages that sometimes take an inordinate amount of time to learn. Plus, R enables a user to carry out complex statistical analyses by simply entering a few commands, making sophisticated analyses available and understandable to a wide audience. Statistical Analysis with R For Dummies enables you to perform these analyses and to fully understand their implications and results. Gets you up to speed on the #1 analytics/data science software tool Demonstrates how to easily find, download, and use cutting-edge community-reviewed methods in statistics and predictive modeling Shows you how R offers intel from leading researchers in data science, free of charge Provides information on using R Studio to work with R Get ready to use R to crunch and analyze your data—the fast and easy way!

OECD Development Pathways Multi-dimensional Review of Lao PDR Financing Sustainable Development

Author : OECD
Publisher : OECD Publishing
ISBN 13 : 9264327789
Total Pages : 330 pages
Book Rating : 4.2/5 (643 download)

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Book Synopsis OECD Development Pathways Multi-dimensional Review of Lao PDR Financing Sustainable Development by : OECD

Download or read book OECD Development Pathways Multi-dimensional Review of Lao PDR Financing Sustainable Development written by OECD and published by OECD Publishing. This book was released on 2024-06-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lao People’s Democratic Republic (Lao PDR) has made significant headway on its development path over the past three decades. The country’s sustained economic growth has been led by booming commodity exports and substantial inflows of external financing. Many Laotians have seen significant improvements in their well-being. Poverty has declined as household income has increased, and many important development goals in education and health have been achieved. In the face of macroeconomic challenges, a shift from commodity-driven growth to a more inclusive prosperity paradigm that emphasises the creation of broad-based opportunities, human capital development and green sustainability can unlock Lao PDR’s future development. This report presents priorities for overcoming the country’s current fiscal constraints and finding ways to fund this shift. Recommendations address strengthening Lao PDR’s sustainable finance and debt management, revenue generation and tax reform, investment promotion, and data capacity in order to tap into green finance mechanisms.

Foundations of Statistics for Data Scientists

Author : Alan Agresti
Publisher : CRC Press
ISBN 13 : 1000462919
Total Pages : 486 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Foundations of Statistics for Data Scientists by : Alan Agresti

Download or read book Foundations of Statistics for Data Scientists written by Alan Agresti and published by CRC Press. This book was released on 2021-11-22 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Statistics for Data Scientists: With R and Python is designed as a textbook for a one- or two-term introduction to mathematical statistics for students training to become data scientists. It is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modeling. The book assumes knowledge of basic calculus, so the presentation can focus on "why it works" as well as "how to do it." Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python. The book also introduces modern topics that do not normally appear in mathematical statistics texts but are highly relevant for data scientists, such as Bayesian inference, generalized linear models for non-normal responses (e.g., logistic regression and Poisson loglinear models), and regularized model fitting. The nearly 500 exercises are grouped into "Data Analysis and Applications" and "Methods and Concepts." Appendices introduce R and Python and contain solutions for odd-numbered exercises. The book's website has expanded R, Python, and Matlab appendices and all data sets from the examples and exercises.

M-statistics

Author : Eugene Demidenko
Publisher : John Wiley & Sons
ISBN 13 : 1119891795
Total Pages : 244 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis M-statistics by : Eugene Demidenko

Download or read book M-statistics written by Eugene Demidenko and published by John Wiley & Sons. This book was released on 2023-08-22 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: M-STATISTICS A comprehensive resource providing new statistical methodologies and demonstrating how new approaches work for applications M-statistics introduces a new approach to statistical inference, redesigning the fundamentals of statistics, and improving on the classical methods we already use. This book targets exact optimal statistical inference for a small sample under one methodological umbrella. Two competing approaches are offered: maximum concentration (MC) and mode (MO) statistics combined under one methodological umbrella, which is why the symbolic equation M=MC+MO. M-statistics defines an estimator as the limit point of the MC or MO exact optimal confidence interval when the confidence level approaches zero, the MC and MO estimator, respectively. Neither mean nor variance plays a role in M-statistics theory. Novel statistical methodologies in the form of double-sided unbiased and short confidence intervals and tests apply to major statistical parameters: Exact statistical inference for small sample sizes is illustrated with effect size and coefficient of variation, the rate parameter of the Pareto distribution, two-sample statistical inference for normal variance, and the rate of exponential distributions. M-statistics is illustrated with discrete, binomial, and Poisson distributions. Novel estimators eliminate paradoxes with the classic unbiased estimators when the outcome is zero. Exact optimal statistical inference applies to correlation analysis including Pearson correlation, squared correlation coefficient, and coefficient of determination. New MC and MO estimators along with optimal statistical tests, accompanied by respective power functions, are developed. M-statistics is extended to the multidimensional parameter and illustrated with the simultaneous statistical inference for the mean and standard deviation, shape parameters of the beta distribution, the two-sample binomial distribution, and finally, nonlinear regression. Our new developments are accompanied by respective algorithms and R codes, available at GitHub, and as such readily available for applications. M-statistics is suitable for professionals and students alike. It is highly useful for theoretical statisticians and teachers, researchers, and data science analysts as an alternative to classical and approximate statistical inference.