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Probability, statistics and simulation : with application programs written in R / / Alberto Rotondi, Paolo Pedroni, and Antonio Pievatolo
| Probability, statistics and simulation : with application programs written in R / / Alberto Rotondi, Paolo Pedroni, and Antonio Pievatolo |
| Autore | Rotondi Alberto |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (643 pages) |
| Disciplina | 519.50285 |
| Collana | Unitext |
| Soggetto topico |
Mathematical statistics
R (Computer program language) Estadística matemàtica R (Llenguatge de programació) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-09429-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNISA-996503552003316 |
Rotondi Alberto
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Probability, statistics and simulation : with application programs written in R / / Alberto Rotondi, Paolo Pedroni, and Antonio Pievatolo
| Probability, statistics and simulation : with application programs written in R / / Alberto Rotondi, Paolo Pedroni, and Antonio Pievatolo |
| Autore | Rotondi Alberto |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (643 pages) |
| Disciplina | 519.50285 |
| Collana | Unitext |
| Soggetto topico |
Mathematical statistics
R (Computer program language) Estadística matemàtica R (Llenguatge de programació) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-09429-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910634035603321 |
|
Rotondi Alberto
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probabilità, Statistica e Simulazione [[electronic resource] ] : Programmi applicativi scritti in R / / by Alberto Rotondi, Paolo Pedroni, Antonio Pievatolo
| Probabilità, Statistica e Simulazione [[electronic resource] ] : Programmi applicativi scritti in R / / by Alberto Rotondi, Paolo Pedroni, Antonio Pievatolo |
| Autore | Rotondi Alberto |
| Edizione | [4th ed. 2021.] |
| Pubbl/distr/stampa | Milano : , : Springer Milan : , : Imprint : Springer, , 2021 |
| Descrizione fisica | 1 online resource (XV, 621 pagg. 130 figg., 12 figg. a colori.) |
| Disciplina | 519 |
| Collana | La Matematica per il 3+2 |
| Soggetto topico |
Statistics
Measurement Measuring instruments Probabilities Stochastic processes Computer science—Mathematics Mathematical statistics Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences Measurement Science and Instrumentation Probability Theory Stochastic Processes Probability and Statistics in Computer Science Estadística matemàtica Probabilitats Mètodes de simulació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 88-470-4010-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Nota di contenuto | 1 La probabilità -- 2 Rappresentazione dei fenomeni aleatori -- 3 Calcolo elementare delle probabilità -- 4 Calcolo delle probabilità per più variabili -- 5 Funzioni di variabili aleatorie -- 6 Statistica di base: stime -- 7 Statistica di base: verifica di ipotesi -- 8 Il metodo Monte Carlo -- 9 Applicazioni del metodo Monte Carlo -- 10 Inferenza statistica e verosimiglianza -- 11 Minimi quadrati -- 12 Analisi dei dati sperimentali. |
| Record Nr. | UNISA-996466396503316 |
|
Rotondi Alberto
|
||
| Milano : , : Springer Milan : , : Imprint : Springer, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Probabilità, Statistica e Simulazione : Programmi applicativi scritti in R / / by Alberto Rotondi, Paolo Pedroni, Antonio Pievatolo
| Probabilità, Statistica e Simulazione : Programmi applicativi scritti in R / / by Alberto Rotondi, Paolo Pedroni, Antonio Pievatolo |
| Autore | Rotondi Alberto |
| Edizione | [4th ed. 2021.] |
| Pubbl/distr/stampa | Milano : , : Springer Milan : , : Imprint : Springer, , 2021 |
| Descrizione fisica | 1 online resource (XV, 621 pagg. 130 figg., 12 figg. a colori.) |
| Disciplina | 519 |
| Collana | La Matematica per il 3+2 |
| Soggetto topico |
Statistics
Measurement Measuring instruments Probabilities Stochastic processes Computer science—Mathematics Mathematical statistics Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences Measurement Science and Instrumentation Probability Theory Stochastic Processes Probability and Statistics in Computer Science Estadística matemàtica Probabilitats Mètodes de simulació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 88-470-4010-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Nota di contenuto | 1 La probabilità -- 2 Rappresentazione dei fenomeni aleatori -- 3 Calcolo elementare delle probabilità -- 4 Calcolo delle probabilità per più variabili -- 5 Funzioni di variabili aleatorie -- 6 Statistica di base: stime -- 7 Statistica di base: verifica di ipotesi -- 8 Il metodo Monte Carlo -- 9 Applicazioni del metodo Monte Carlo -- 10 Inferenza statistica e verosimiglianza -- 11 Minimi quadrati -- 12 Analisi dei dati sperimentali. |
| Record Nr. | UNINA-9910495347803321 |
|
Rotondi Alberto
|
||
| Milano : , : Springer Milan : , : Imprint : Springer, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||