Mathematical and statistical software Books

Book SynopsisThis book illustrates the capabilities of Microsoft Excel to teach applied statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical statistical problems in industry. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in statistics courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past.The 2nd edition of Applied Business Statistics for Business and Management capitalizes on these improvements by teaching students and practitioners how to apply Excel to statistical techniques necessary in their courses and workplace. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand business problems. Practice problems are provided at the end of each chapter with their solutions.Table of Contents​Statistics and Data.- Summarizing Data.- Descriptive Statistics and Graphing.- Normal World.- Survey Design.- Sampling.- Inference.- Probability.- Correlation.- Simple Linear Regression.- Multiple Regression.- Significance Tests.- Non Linear Regression.- Survey Reports​.

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Book SynopsisThis book and app is for practitioners, professionals, researchers, and students who want to learn how to make a plot within the R environment using ggplot2, step-by-step without coding.In widespread use in the statistical communities, R is a free software language and environment for statistical programming and graphics. Many users find R to have a steep learning curve but to be extremely useful once overcome. ggplot2 is an extremely popular package tailored for producing graphics within R but which requires coding and has a steep learning curve itself, and Shiny is an open source R package that provides a web framework for building web applications using R without requiring HTML, CSS, or JavaScript. This manual—"integrating" R, ggplot2, and Shiny—introduces a new Shiny app, Learn ggplot2, that allows users to make plots easily without coding. With the Learn ggplot2 Shiny app, users can make plots using ggplot2 without having to code each step, reducing typos and error messages and allowing users to become familiar with ggplot2 code. The app makes it easy to apply themes, make multiplots (combining several plots into one plot), and download plots as PNG, PDF, or PowerPoint files with editable vector graphics. Users can also make plots on any computer or smart phone.Learn ggplot2 Using Shiny App allows users to Make publication-ready plots in minutes without coding Download plots with desired width, height, and resolution Plot and download plots in png, pdf, and PowerPoint formats, with or without R code and with editable vector graphics Table of Contents

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Book SynopsisThis textbook is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning.With careful treatment of topics that fill the curricular needs for the course, Probability and Statistics for Computer Science features:• A treatment of random variables and expectations dealing primarily with the discrete case.• A practical treatment of simulation, showing how many interesting probabilities and expectations can be extracted, with particular emphasis on Markov chains.• A clear but crisp account of simple point inference strategies (maximum likelihood; Bayesian inference) in simple contexts. This is extended to cover some confidence intervals, samples and populations for random sampling with replacement, and the simplest hypothesis testing.• A chapter dealing with classification, explaining why it’s useful; how to train SVM classifiers with stochastic gradient descent; and how to use implementations of more advanced methods such as random forests and nearest neighbors.• A chapter dealing with regression, explaining how to set up, use and understand linear regression and nearest neighbors regression in practical problems.• A chapter dealing with principal components analysis, developing intuition carefully, and including numerous practical examples. There is a brief description of multivariate scaling via principal coordinate analysis. • A chapter dealing with clustering via agglomerative methods and k-means, showing how to build vector quantized features for complex signals.Illustrated throughout, each main chapter includes many worked examples and other pedagogical elements such as boxed Procedures, Definitions, Useful Facts, and Remember This (short tips). Problems and Programming Exercises are at the end of each chapter, with a summary of what the reader should know. Instructor resources include a full set of model solutions for all problems, and an Instructor's Manual with accompanying presentation slides.Table of Contents1 Notation and conventions 9 1.0.1 Background Information........................................................................ 10 1.1 Acknowledgements................................................................................................. 11 I Describing Datasets ; 12 2 First Tools for Looking at Data 13 2.1 Datasets....................................................................................................................... 13 2.2 What’s Happening? - Plotting Data................................................................. 15 2.2.1 Bar< Charts.................................................................................................... 16 2.2.2 Histograms................................................................................................... 16 2.2.3 How to Make Histograms...................................................................... 17 2.2.4 Conditional Histograms.......................................................................... 19 2.3 Summarizing 1D Data............................................................................................ 19 2.3.1 The Mean...................................................................................................... 20 2.3.2 Standard Deviation................................................................................... 22 2.3.3 Computing Mean and Standard Deviation Online...................... 26 2.3.4 Variance......................................................................................................... 26 2.3.5 The Median.................................................................................................. 27 2.3.6 Interquartile Range.................................................................................. 29 2.3.7 Using Summaries Sensibly.................................................................... 30 2.4 Plots and Summaries............................................................................................. 31 2.4.1 Some Properties of Histograms.......................................................... 31 2.4.2 Standard Coordinates and Normal Data......................................... 34 2.4.3 Box Plots....................................................................................................... 38 2.5 Whose is bigger? Investigating Australian Pizzas...................................... 39 2.6 You should.................................................................................................................. 43 2.6.1 remember these definitions:................................................................. 43 2.6.2 remember these terms............................................................................ 43 2.6.3 remember these facts:............................................................................. 43 2.6.4 be able to...................................................................................................... 43 3 Looking at Relationships 47 3.1 Plotting 2D Data...................................................................................................... 47 3.1.1 3.1.2 Series.............................................................................................................. 51 3.1.3 Scatter Plots for Spatial Data.............................................................. 53 3.1.4 Exposing Relationships with Scatter Plots..................................... 54 3.2 Correlation.................................................................................................................. 57 3.2.1 The Correlation Coefficient................................................................... 60 3.2.2 Using Correlation to Predict................................................................ 64 3.2.3 Confusion caused by correlation......................................................... 68 1 <3.3 Sterile Males in Wild Horse Herds.................................................................. 68 3.4 You should.................................................................................................................. 72 3.4.1 remember these definitions:................................................................. 72 3.4.2 remember these terms............................................................................ 72 3.4.3 remember these facts: . . . . . 3.4.4 use these procedures: . . . . . . 3.4.5 be able to: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . . . . . . . . . . . 72 . . . . . . . . . . . . . . . . . 72 II Probability &nbsp; 78 4 Basic ideas in probability 79 4.1 Experiments, Outcomes and Probability....................................................... 79 4.1.1 Outcomes and Probability...................................................................... 79 4.2 Events........................................................................................................................... 81 4.2.1 Computing Event Probabilities by Counting Outcomes............. 83 4.2.2 The Probability of Events...................................................................... 87 4.2.3 Computing Probabilities by Reasoning about Sets...................... 89 4.3 Independence............................................................................................................ 92 4.3.1 Example: Airline Overbooking............................................................ 96 4.4 Conditional ........................................................ 99 4.4.1 Evaluating Conditional Probabilities.............................................. 100 4.4.2 Detecting Rare Events is Hard......................................................... 104 4.4.3 Conditional Probability and Various Forms of Independence . 106 4.4.4 The Prosecutor’s Fallacy 108 4.4.5 Example: The Monty Hall Problem................................................ 110 4.5 Extra Worked Examples.................................................................................... 112 4.5.1 Outcomes and Probability................................................................... 112 4.5.2 Events.......................................................................................................... 114 4.5.3 Independence........................................................................................... 115 4.5.4 Conditional Probability......................................................................... 117 4.6 You should............................................................................................................... 121 4.6.1 remember these definitions:.............................................................. 121 4.6.2 remember these terms......................................................................... 121 4.6.3 remember and use these facts.......................................................... 121 4.6.4 remember these points:....................................................................... 121 4.6.5 be able to.................................................................................................... 121 5 Random Variables and Expectations 128 5.1 Random Variables................................................................................................. 128 5.1.1 Joint and Conditional Probability for Random Variables . . . 131 5.1.2 Just a Little Continuous Probability............................................... 134 5.2 Expectations and Expected Values................................................................ 137 5.2.1 Expected Values...................................................................................... 138 5.2.2 Mean, Variance and Covariance....................................................... 141 5.2.3 Expectations and Statistics................................................................. 145 5.3 The Weak Law of Large Numbers................................................................ 145 5.3.1 IID Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.3.2 Two Inequalities . . . . . . . . . . . . . . . . . . . . . . . .< . 146 5.3.3 Proving the Inequalities . . . . . . . . . . . . . . . . . . . . . 147 5.3.4 The Weak Law of Large Numbers.................................................. 149 5.4 Using the Weak Law of Large Numbers 151 5.4.1 Should you accept a bet?..................................................................... 151 5.4.2 Odds, Expectations and Bookmaking — a Cultural Diversion 152 5.4.3 Ending a Game Early 154 5.4.4 Making a Decision with Decision Trees and Expectations . . 154 5.4.5 Utility 156 5.5 You should................................................................................... 159 5.5.1 remember these definitions:.............................................................. 159 5.5.2 remember these terms......................................................................... 159 5.5.3 use and remember these facts.......................................................... 159 5.5.4 be able to.................................................................................................... 160 6 Useful Probability Distributions ; 167 6.1 Discrete Distributions 167 6.1.1 The Discrete Uniform Distribution................................................. 167 6.1.2 Bernoulli Random Variables............................................................... 168 6.1.3 The Geometric Distribution................................................................ 168 6.1.4 The Binomial Probability Distribution........................................... 169 6.1.5 Multinomial probabilities..................................................................... 171 6.1.6 The Poisson Distribution..................................................................... 172 6.2 Continuous Distributions ; 174 6.2.1 The Continuous Uniform Distribution........................................... 174 6.2.2 The Beta Distribution........................................................................... 174 6.2.3 The Gamma Distribution..................................................................... 176 6.2.4 The Exponential Distribution............................................................ 176 6.3 The Normal Distribution ; 178 6.3.1 The Standard Normal Distribution................................................. 178 6.3.2 The Normal Distribution..................................................................... 179 6.3.3 Properties of The Normal Distribution......................................... 180 6.4 Approximating Binomials with Large N 182 6.4.1 Large N....................................................................................................... 183 6.4.2 Getting Normal<........................................................................................ 185 6.4.3 Using a Normal Approximation to the Binomial Distribution 187 6.5 You should . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 remember these definitions: . . . . . . . . . . . . . . . . 6.5.2 remember these terms: . . . . . . . . . . . . . . . . . . . 6.5.3 remember these facts: . . . . . . . . . . . . . . . . . . . 6.5.4 remember these points: . . . . . . . . . . . . . . . . . .< . . . 188 . . . 188 . . . 188 . . . 188 . . . 188 III Inference ; 196 7 Samples and Populations 197 7.1 The Sample Mean................................................................................................. 197 7.1.1 The Sample Mean is an Estimate of the Population Mean . . 197 7.1.2 The Variance of the Sample Mean.................................................. 198 7.1.3 When The Urn Model Works............................................................ 201 7.1.4 Distributions are Like Populations................................................. 202 7.2 Confidence Intervals............................................................................................ 203 7.2.1 Constructing Confidence Intervals.................................................. 203 7.2.2 Estimating the Variance of the Sample Mean............................ 204 7.2.3 The Probability Distribution of the Sample Mean..................... 206 &lt;7.2.4 Confidence Intervals for Population Means................................. 208 7.2.5 Standard Error Estimates from Simulation................................. 212 7.3 You should............................................................................................................... 216 7.3.1 remember these definitions:.............................................................. 216 7.3.2 remember these terms......................................................................... 216 7.3.3 remember these facts:........................................................................... 216 7.3.4 use these procedures............................................................................. 216 7.3.5 be able to.................................................................................................... 216 8 The Significance of Evidence 221 8.1 Significance.............................................................................................................. 222 8.1.1 Evaluating Significance......................................................................... 223 8.1.2 P-values....................................................................................................... 225 8.2 Comparing the Mean of Two Populations.................................................. 230 8.2.1 Assuming Known Population Standard Deviations................... 231 8.2.2 Assuming Same, Unknown Population Standard Deviation . 233 8.2.3 Assuming Different, Unknown Population Standard Deviation 235 8.3 Other Useful Tests of Significance................................................................. 237 8.3.1 F-tests and Standard Deviations...................................................... 237 8.3.2 χ2 Tests of Model Fit............................................................................ 239 8.4 Dangerous Behavior............................................................................................. 244 8.5 You should............................................................................................................... 246 8.5.1 remember these definitions:.............................................................. 246 8.5.2 remember 8.5.3 remember these facts: . . . . . 8.5.4 use these procedures: . . . . . . 8.5.5 be able to: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 . . . . . . . . . . . . . . . . . 246 . . . . . . . . . . . . . . . . . 246 9 Experiments &nbsp; 251 9.1 A Simple Experiment: The Effect of a Treatment.................................. 251 9.1.1 Randomized Balanced Experiments............................................... 252 9.1.2 Decomposing Error in Predictions.................................................. 253 9.1.3 Estimating the Noise Variance......................................................... 253 9.1.4 The ANOVA Table.................................................................................. 255 9.1.5 Unbalanced Experiments.................................................................... 257 9.1.6 Significant Differences.......................................................................... 259 9.2 Two Factor Experiments.................................................................................... 261 9.2.1 &nbsp; Decomposing the Error........................................................................ 264 9.2.2 Interaction Between Effects................................................................ 265 9.2.3 The Effects of a Treatment................................................................. 266 9.2.4 Setting up an ANOVA Table.............................................................. 267 9.3 You should............................................................................................................... 272 9.3.1 remember these definitions:.............................................................. 272 9.3.2 remember these terms......................................................................... 272 9.3.3 remember these facts:........................................................................... 272 9.3.4 use these procedures............................................................................. 272 9.3.5 be able to.................................................................................................... 272 9.3.6 Two-Way Experiments.......................................................................... 274 10 Inferring Probability Models from Data &nbsp; 275 10.1 Estimating Model Parameters with Maximum Likelihood.................. 275 10.1.1 The Maximum Likelihood Principle............................................... 277 10.1.2 Binomial, Geometric and Multinomial Distributions................ 278 10.1.3 Poisson and Normal Distributions................................................... 281 10.1.4 Confidence Intervals for Model Parameters................................ 286 10.1.5 Cautions about Maximum Likelihood............................................ 288 10.2 Incorporating Priors with Bayesian Inference.......................................... 289 10.2.1 Conjugacy................................................................................................... 292 10.2.2 MAP Inference......................................................................................... 294 10.2.3 Cautions about Bayesian Inference................................................. 296 10.3 Bayesian Inference for Normal Distributions............................................ 296 10.3.1 Example: Measuring Depth of a Borehole................................... 296 10.3.2 Normal Prior and Normal Likelihood Yield Normal Posterior 297 10.3.3 Filtering...................................................................................................... 300 10.4 You should............................................................................................................... 303 10.4.1 remember these definitions:.............................................................. 303 10.4.2 remember these terms......................................................................... 303 10.4.3 remember these facts:........................................................................... 304 10.4.4 use these procedures............................................................................. 304 10.4.5 be able to.................................................................................................... 304 &lt;IV Tools 312 11 Extracting Important Relationships in High Dimensions 313 11.1 Summaries and Simple Plots........................................................................... 313 11.1.1 The Mean................................................................................................... 314 11.1.2 Stem Plots and Scatterplot Matrices.............................................. 315 11.1.3 Covariance.................................................................................................. 317 11.1.4 The Covariance Matrix......................................................................... 319 11.2 Using Mean and Covariance to Understand High Dimensional Data . 321 11.2.1 Mean and Covariance under Affine Transformations............... 322 11.2.2 . . 324 . . 325 . . 326 . . 327 . . 329 . 332 . . 334 . . 335 . . 335 . . 338 . . 339 . . 341 . . < 345 . . 345 . . 345 . . 345 . . 345 . . 345 349 . . 349 . . 350 . . 350 . . 351 . . 351 . . 353 . . 355 . . 357 . . 358 . . 359 . . <360 .< . 361 < Eigenvectors and Diagonalization . . . . . . . . . . . . . . 11.2.3 Diagonalizing Covariance by Rotating Blobs . . . . . . . . 11.2.4 Approximating Blobs . . . . . . . . . . . . . . . . . . . . 11.2.5 Example: Transforming the Height-Weight Blob . . . . . 11.3 Principal Components Analysis . . . . . . . . . . . . . . . . . . . 11.3.1 Example: Representing Colors with Principal Components 11.3.2 Example: Representing Faces with Principal Components 11.4 Multi-Dimensional Scaling . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Choosing Low D Points using High D Distances . . . . . . 11.4.2 Factoring a Dot-Product Matrix . . . . . . . . . . . . . . 11.4.3 Example: Mapping with Multidimensional Scaling . . . . 11.5 Example: Understanding Height and Weight . . . . . . . . . . . 11.6 You should . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6.1 remember these definitions: . . . . . . . . . . . . . . . . . 11.6.2 remember these terms: . . . . . . . . . . . . . . . . . . . . 11.6.3 remember these facts: .&nbsp; . . . . . . . . . . . . . . . . . . . 11.6.4 use these procedures: . . . . . . . . . . . . . . . . . . . . . 11.6.5 be able to: . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Learning to Classify 12.1 Classification: The Big Ideas . . . . . . . . . . . . . . . . . . . . 12.1.1 The Error Rate . . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Overfitting . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.3 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . 12.1.4 Is the Classifier Working Well? . . . . . . . . . . . . . . . 12.2 Classifying with Nearest Neighbors . . . . . . . . . . . . . . . . . 12.3 Classifying with Naive Bayes . . . . . . . . . . . . . . . . . . . . 12.3.1 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 The Support 12.4.1 Choosing a Classifier with the Hinge Loss . . . . . . . . . 12.4.2 Finding a Minimum: General Points . . . . . . . . . . . . 12.4.3 Finding a Minimum: Stochastic Gradient Descent . . . . 12.4.4 Example: Training an SVM with Stochastic Gradient Descent 363 12.4.5 Multi-Class Classification with SVMs.............................................. 366 12.5 Classifying with Random Forests................................................................... 367 12.5.1 Building a Decision Tree..................................................................... 367 12.5.2 Choosing a Split with Information Gain........................................ 370 12.5.3 Forests......................................................................................................... 373 12.5.4 Building and Evaluating a Decision Forest.................................. 374 12.5.5 Classifying Data Items with a Decision Forest........................... 375 12.6 You should............................................................................................................... 378 12.6.1 remember these definitions:.............................................................. 378 12.6.2 remember these terms......................................................................... 378 12.6.3 remember these facts:........................................................................... 379 12.6.4 use these procedures............................................................................. 379 12.6.5 be able to.................................................................................................... 379 < 13.1 The Curse of Dimension..................................................................................... 384 13.1.1 The Curse: Data isn’t Where You Think it is............................. 384 13.1.2 Minor Banes of Dimension.................................................................. 386 13.2 The Multivariate Normal Distribution......................................................... 387 13.2.1 Affine Transformations and Gaussians.......................................... 387 13.2.2 Plotting a 2D Gaussian: Covariance Ellipses.............................. 388 13.3 Agglomerative and Divisive Clustering........................................................ 389 13.3.1 Clustering and Distance....................................................................... 391 13.4 &nbsp; The K-Means Algorithm and Variants......................................................... 392 13.4.1 How to choose K...................................................................................... 395 13.4.2 Soft Assignment....................................................................................... 397 13.4.3 General Comments on K-Means....................................................... 400 13.4.4 K-Mediods.................................................................................................. 400 13.5 Application Example: Clustering Documents........................................... 401 13.5.1 A Topic Model.......................................................................................... 402 13.6 Describing Repetition with Vector Quantization...................................... 403 13.6.1 Vector Quantization............................................................................... 404 13.6.2 Example: Groceries in Portugal....................................................... 406 13.6.3 Efficient Clustering and Hierarchical K Means.......................... 409 13.6.4 Example: Activity from Accelerometer Data............................... 409 13.7 You should............................................................................................................... 413 13.7.1 remember these definitions:.............................................................. 413 13.7.2 remember these terms......................................................................... 413 13.7.3 remember these facts:........................................................................... 413 13.7.4 use these procedures............................................................................. 413 14 Regression &nbsp; 417 14.1.1 Regression to Make Predictions....................................................... 417 14.1.2 Regression to Spot Trends.................................................................. 419 14.1 Linear Regression and Least Squares.......................................................... 421 14.1.1 Linear Regression................................................................................... 421 14.1.2 Choosing β.................................................................................................. 422 14.1.3 Solving the Least Squares Problem................................................ 423 14.1.4 &nbsp; Residuals..................................................................................................... 424 14.1.5 R-squared.................................................................................................... 424 14.2 Producing Good Linear Regressions............................................................. 427 14.2.1 Transforming Variables........................................................................ 428 14.2.2 Problem Data Points have Significant Impact............................ 431 14.2.3 Functions of One Explanatory Variable........................................ 433 14.2.4 Regularizing Linear Regressions...................................................... 435 14.3 &nbsp; Exploiting Your Neighbors 14.3.1 Using your Neighbors to Predict More than a Number............ 441 14.3.2 Example: Filling Large Holes with Whole Images.................... 441 14.4 You should . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.1 remember these definitions: . . . . . . . . . . . . . . 14.4.2 remember these terms: . . . . . . . . . . . . . . . . . . . . . . 444 . . . . . 444 . . . . . 444 14.4.3 remember these facts:........................................................................... 444 14.4.4 remember these procedures:............................................................. 444 15 Markov Chains and Hidden Markov Models &nbsp; 454 15.1 Markov Chains........................................................................................................ 454 15.1.1 Transition Probability Matrices........................................................ 457 15.1.2 Stationary Distributions....................................................................... 459 15.1.3 Example: Markov Chain Models of Text...................................... 462 15.2 Estimating Properties of Markov Chains.................................................... 465 15.2.1 Simulation.................................................................................................. 465 15.2.2 Simulation Results as Random Variables..................................... 467 15.2.3 Simulating Markov Chains.................................................................. 469 15.3 Example: Ranking the Web by Simulating a Markov Chain................ 472 15.4 Hidden Markov Models and Dynamic Programming............................. 473 15.4.1 Hidden Markov Models........................................................................ 474 15.4.2 Picturing Inference with a Trellis.................................................... 474 15.4.3 Dynamic Programming for HMM’s: Formalities....................... 478 15.4.4 &nbsp; Example: Simple Communication Errors..................................... 478 15.5 You should............................................................................................................... 481 15.5.1 remember these definitions:.............................................................. 481 15.5.2 remember these terms......................................................................... 481 15.5.3 remember these facts:........................................................................... 481 15.5.4 be able to.................................................................................................... 481 V Some Mathematical Background &nbsp; 484 16 Resources 485 16.1 Useful Material about Matrices....................................................................... 485 16.1.1 The Singular Value Decomposition................................................. 486 16.1.2 Approximating A Symmetric Matrix............................................... 487 16.2 Some Special Functions..................................................................................... 489 16.3 Finding Nearest Neighbors............................................................................... 490 16.4 Entropy and Information Gain........................................................................ 493

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Book SynopsisChristine Duller gibt in diesem Buch eine leicht verständliche Einführung in die nichtparametrische Statistik. Dabei beschreibt sie nicht nur die statistischen Verfahren, sondern setzt diese auch in SAS und R um. Beide Programmiersprachen stellt die Autorin kurz vor, sodass keine Vorkenntnisse notwendig sind. Das Buch eignet sich besonders für Studierende der Wirtschafts- und Sozialwissenschaften und alle Interessierten, die (nur) über Grundkenntnisse der Statistik verfügen, aber auch als Nachschlagewerk für einfache statistische Analysen.Table of ContentsStatistische Grundbegriffe.- Geordnete Statistiken und Rangstatistiken.- Einstichprobenprobleme.- Unabhängigkeit und Korrelation.- Zweistichprobenprobleme für unabhängige Stichproben.- Zweistichprobenprobleme für verbundene Stichproben.- c-Stichproben-Problem. Nichtparametrische Dichteschätzung.- Lösungen zu den Übungsaufgaben.- Tabellen.- Sachverzeichnis.

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Book Synopsis​The objective of this text is to introduce RStudio to practitioners and students and enable them to use R in their everyday work. It is not a statistical textbook, the purpose is to transmit the joy of analyzing data with RStudio. Practitioners and students learn how RStudio can be installed and used, they learn to import data, write scripts and save working results. Furthermore, they learn to employ descriptive statistics and create graphics with RStudio. Additionally, it is shown how RStudio can be used to test hypotheses, run an analysis of variance and regressions. To deepen the learned content, tasks are included with the solutions provided at the end of the textbook. This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.Trade Review“This book can be used for self-study by those in business administration, engineering, and the social, health, or biological science fields, to become competent in statistical programming. … it can be used as supplementary material for statistics-related courses. … Each chapter ends with a summary of R commands and appropriate exercises. Moreover, the appendix presents detailed code solutions to facilitate faster code-learning among readers. … this book can evoke readers’ interests in analyzing data and reduce the learning difficulty.” (Mei-Hsien Lee, Biometrics, Vol. 77 (4), December, 2021)“I enjoyed reading this book. The authors were good at creating a complete tool for beginners to start along the path of essential statistical analysis in R. I recommend this book, for its content, writing, and organization, to undergraduate or graduate students of disciplines other than statistics but also to professionals (non-statisticians) who would like to acquire or improve their analysis skills and understand the depth of R functionality, especially nowadays that R use is very popular among data analysts.” (Georgios Nikolopoulos, ISCB News, iscb.info, Vol. 72, December, 2021)Table of ContentsComment.- 1 R and RStudio.- 2 Data analysis basics with RStudio.- 3 Data tourism (simulated).- 4 Describing data with RStudio.- 5 Testing normal distribution with RStudio.- 6 Testing hypotheses with RStudio,- 7 Linear regression with RStudio.- 8 Further reading.- 9 Appendix: 1 Questionnaire, 2 Data "tourism.xlsx" including legend, 3 How to deal with missing data, 4 Solutions for the task.

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Book Synopsis

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Book SynopsisStatistics is more topical than ever. Numerous decisions depend on statistical considerations: just think of the Corona crisis or decisions about approving new drugs or other products. If researchers announce they have proved some fact using statistical tests, can we then always be sure that their claim is correct? How, and more importantly why, does statistics work? What can we expect from statistics and what not? 'Fact or Fluke?' is not a textbook that explains statistical tests to the reader; instead, it discusses what comes before those tests: the philosophy behind the statistics. Should one carry out tests, or are there other ways to look at statistics? Ronald Meester and Klaas Slooten use a variety of examples – from court cases to theoretical physics – to present different views on statistics and provide arguments for what they think is the best point of view. This book is meant for anyone who is in some way concerned with, or interested in, statistical evidence: scientific researchers, students, teachers, mathematicians, philosophers, lawyers, managers, and no doubt many others.

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Book SynopsisRecent advances in the understanding of star formation and evolution have been impressive and aspects of that knowledge are explored in this volume. The black hole stellar endpoints are studied and geodesic motion is explored. The emission of gravitational waves is featured due to their very recent experimental discovery.The second aspect of the text is space exploration which began 62 years ago with the Sputnik Earth satellite followed by the landing on the Moon just 50 years ago. Since then Mars has been explored remotely as well as flybys of the outer planets and probes which have escaped the solar system. The text explores many aspects of rocket travel. Finally possibilities for interstellar travel are discussed.All these topics are treated in a unified way using the Matlab App to combine text, figures, formulae and numeric input and output. In this way the reader may vary parameters and see the results in real time. That experience aids in building up an intuitive feel for the many specific problems given in this text.

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Book SynopsisRecent advances in the understanding of star formation and evolution have been impressive and aspects of that knowledge are explored in this volume. The black hole stellar endpoints are studied and geodesic motion is explored. The emission of gravitational waves is featured due to their very recent experimental discovery.The second aspect of the text is space exploration which began 62 years ago with the Sputnik Earth satellite followed by the landing on the Moon just 50 years ago. Since then Mars has been explored remotely as well as flybys of the outer planets and probes which have escaped the solar system. The text explores many aspects of rocket travel. Finally possibilities for interstellar travel are discussed.All these topics are treated in a unified way using the Matlab App to combine text, figures, formulae and numeric input and output. In this way the reader may vary parameters and see the results in real time. That experience aids in building up an intuitive feel for the many specific problems given in this text.

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Book SynopsisThis workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.

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Book SynopsisThis workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.

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Book SynopsisThis is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.Table of ContentsR Preliminaries; Elementary Geometry and Algebra Using R; Vector Spaces; Matrix Basics and R Software; Determinant and Singularity; The Rank and Trace of a Matrix; Matrix Inverse and Solution of Linear Equations.

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Book SynopsisThis is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.Table of ContentsR Preliminaries; Elementary Geometry and Algebra Using R; Vector Spaces; Matrix Basics and R Software; Determinant and Singularity; The Rank and Trace of a Matrix; Matrix Inverse and Solution of Linear Equations.

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Book SynopsisPAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a “manual” giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.Table of ContentsIntroduction; Using PAMIR; Benchmark Examples and Comparisons; Computational Integration Theory and PAMIR; Details of Construction of the PAMIR Algorithms and Programs; Appendices: Test Integrals; Derivation of the Simplex Generating Function; Derivation of the Hypercube Generating Function; Mappings Between Base Regions; Rule for Determining Where a Point Lies with Respect to a Simplex; Expansion for ∑4; Fourth Order Simplex Formula; Ninth Order Simplex Formula; Ninth Order Hypercube Formula.

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Book SynopsisPAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a “manual” giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.Table of ContentsIntroduction; Using PAMIR; Benchmark Examples and Comparisons; Computational Integration Theory and PAMIR; Details of Construction of the PAMIR Algorithms and Programs; Appendices: Test Integrals; Derivation of the Simplex Generating Function; Derivation of the Hypercube Generating Function; Mappings Between Base Regions; Rule for Determining Where a Point Lies with Respect to a Simplex; Expansion for ∑4; Fourth Order Simplex Formula; Ninth Order Simplex Formula; Ninth Order Hypercube Formula.

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Book SynopsisThis text continues the exploration of the use of MATLAB tools and features in visualizing physical processes. The symbolic math packages are important in solving those problems which are amenable to closed form solution, while the numerical packages are used for the remaining problems. The results for the solutions use the MATLAB graphics packages to help visualize the properties of the solutions. User dialogues are designed to allow users to change the input parameters in order to see how the dynamics of the solutions depends on the parameters of the specific problem. In particular movies are used to display the dynamical evolution of solutions in time.Table of ContentsMathematics; Classical Mechanics; Electromagnetism; Gases and Fluids; Waves; Quantum Mechanics; Astrophysics; General Relativity;

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