Probability, statistics and simulation : with application programs written in R / / Alberto Rotondi, Paolo Pedroni, and Antonio Pievatolo

• Autore: Rotondi Alberto
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (643 pages)
• Disciplina: 519.50285
• Soggetto topico: Mathematical statistics; R (Computer program language); Estadística matemàtica; R (Llenguatge de programació)
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): PedroniPaolo; PievatoloAntonio
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- How to Use the Text -- Contents -- About the Authors -- 1 Probability -- 1.1 Chance, Chaos and Determinism -- 1.2 Some Basic Terms -- 1.3 The Concept of Probability -- 1.4 Axiomatic Probability -- 1.5 Repeated Trials -- 1.6 Elements of Combinatorial Analysis -- 1.7 Bayes' Theorem -- 1.8 Learning Algorithms -- 1.9 Problems -- 2 Representation of Random Phenomena -- 2.1 Introduction -- 2.2 Random Variables -- 2.3 Cumulative or Distribution Function -- 2.4 Data Representation -- 2.5 Discrete Random Variables -- 2.6 Binomial Distribution -- 2.7 Continuous Random Variables -- 2.8 Mean, Sum of Squares, Variance, Standard Deviation and Quantiles -- 2.9 Operators -- 2.10 Simple Random Sample -- 2.11 Convergence Criteria -- 2.12 Problems -- 3 Basic Probability Theory -- 3.1 Introduction -- 3.2 Properties of the Binomial Distribution -- 3.3 Poisson Distribution -- 3.4 Normal or Gaussian Density -- 3.5 The Three-Sigma Law and the Standard Gaussian Density -- 3.6 Central Limit Theorem and Universality of the GaussianCurve -- 3.7 Poisson Stochastic Processes -- 3.8 χ2 Density -- 3.9 Uniform Density -- 3.10 Chebyshev's Inequality -- 3.11 How to Use Probability Calculus -- 3.12 Problems -- 4 Multivariate Probability Theory -- 4.1 Introduction -- 4.2 Multivariate Statistical Distributions -- 4.3 Covariance and Correlation -- 4.4 Two-Dimensional Gaussian Distribution -- 4.5 The General Multidimensional Case -- 4.6 Multivariate Probability Regions -- 4.7 Multinomial Distribution -- 4.8 Problems -- 5 Functions of Random Variables -- 5.1 Introduction -- 5.2 Functions of a Random Variable -- 5.3 Functions of Several Random Variables -- 5.4 Mean and Variance Transformation -- 5.5 Means and Variances for n Variables -- 5.6 Problems -- 6 Basic Statistics: Parameter Estimation -- 6.1 Introduction -- 6.2 Confidence Intervals. ; 6.3 Confidence Intervals with Pivotal Variables -- 6.4 Mention of the Bayesian Approach -- 6.5 Some Notations -- 6.6 Probability Estimation -- 6.7 Probability Estimation from Large Samples -- 6.8 Poissonian Interval Estimation -- 6.9 Mean Estimation from Large Samples -- 6.10 Variance Estimation from Large Samples -- 6.11 Mean and Variance Estimation for Gaussian Samples -- 6.12 How to Use the Estimation Theory -- 6.13 Estimates from a Finite Population -- 6.14 Histogram Analysis -- 6.15 Estimation of the Correlation -- 6.16 Problems -- 7 Basic Statistics: Hypothesis Testing -- 7.1 Testing One Hypothesis -- 7.2 The Gaussian z-Test -- 7.3 Student's t-Test -- 7.4 Chi-Square Test -- 7.5 Compatibility Check Between Sample and Population -- 7.6 Hypothesis Testing with Contingency Tables -- 7.7 Multiple Tests -- 7.8 Snedecor's F-Test -- 7.9 Analysis of Variance (ANOVA) -- 7.10 Two-Way ANOVA -- 7.11 Problems -- 8 Monte Carlo Methods -- 8.1 Introduction -- 8.2 What Is Monte Carlo? -- 8.3 Mathematical Aspects -- 8.4 Generation of Discrete Random Variables -- 8.5 Generation of Continuous Random Variables -- 8.6 Linear Search Method -- 8.7 Rejection Method -- 8.8 Particular Random Generation Methods -- 8.9 Monte Carlo Analysis of Distributions -- 8.10 Evaluation of Confidence Intervals -- 8.11 Simulation of Counting Experiments -- 8.12 Non-parametric Bootstrap -- 8.13 Hypothesis Test with Simulated Data -- 8.14 Problems -- 9 Applications of Monte Carlo Methods -- 9.1 Introduction -- 9.2 Study of Diffusion Phenomena -- 9.3 Simulation of Stochastic Processes -- 9.4 Number of Workers in a Plant: Synchronous Simulation -- 9.5 Number of Workers in a Plant: Asynchronous Simulation -- 9.6 Kolmogorov-Smirnov Test -- 9.7 Metropolis Algorithm -- 9.8 Ising Model -- 9.9 Definite Integral Calculation -- 9.10 Importance Sampling -- 9.11 Stratified Sampling. ; 9.12 Multidimensional Integrals -- 9.13 Problems -- 10 Statistical Inference and Likelihood -- 10.1 Introduction -- 10.2 Maximum Likelihood (ML) Method -- 10.3 Estimator Properties -- 10.4 Theorems on Estimators -- 10.5 Confidence Intervals -- 10.6 Least Squares Method and Maximum Likelihood -- 10.7 Best Fit of Densities to Data and Histograms -- 10.8 Weighted Mean -- 10.9 Test of Hypotheses -- 10.10 One- or Two-Sample Tests -- 10.11 Most Powerful Tests -- 10.12 Test Functions -- 10.13 Sequential Tests -- 10.14 Problems -- 11 Least Squares -- 11.1 Introduction -- 11.2 No Errors on Predictors -- 11.3 Errors in Predictors -- 11.4 Least Squares Regression Lines: Unweighted Case -- 11.5 Unweighted Linear Least Squares -- 11.6 Weighted Linear Least Squares -- 11.7 Properties of Least Squares Estimates -- 11.8 Model Testing and Search for Functional Forms -- 11.9 Search for Correlations -- 11.10 Fit Strategies -- 11.11 Nonlinear Least Squares -- 11.12 Problems -- 12 Experimental Data Analysis -- 12.1 Introduction -- 12.2 Terminology -- 12.3 Constant and Variable Physical Quantities -- 12.4 Instrumental Sensitivity and Accuracy -- 12.5 Measurement Uncertainty -- 12.6 Treatment of Systematic Effects -- 12.7 Best Fit with Offset Systematic Errors -- 12.8 Best Fit with Scale Systematic Errors -- 12.9 Indirect Measurements and Error Propagation -- 12.10 Measurement Types -- 12.11 M(0, 0, Δ) Measurements -- 12.12 M(0, σ, 0) Measurements -- 12.13 M(0, σ, Δ) Measurements -- 12.14 M(f, 0, 0) Measurements -- 12.15 M(f, σ, 0), M(f, 0, Δ) and M(f, σ, Δ) Measurements -- 12.16 A Case Study: Millikan's Experiments -- 12.17 Some Remarks on the Scientific Method -- 12.18 Problems -- A Table of Symbols -- B R Software -- C Moment-Generating Functions -- D Solutions of Problems -- E Tables -- E.1 Integral of the Gaussian Density. ; E.2 Quantiles of the Student's Density -- E.3 Integrals of the Reduced χ2 Density -- E.4 Quantile Values of the Non-Reduced χ2 Density -- E.5 Quantiles of the F Density -- Bibliography -- Index.
• Titolo autorizzato: Probability, statistics and simulation
• ISBN: 3-031-09429-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996503552003316
• Lo trovi qui: Univ. di Salerno
• Serie: Unitext