Data Analysis: Statistical and Computational Methods for Scientists and Engineers (Hardcover, 3, 1999)

1 Introduction.- 1.1 Typical Problems of Data Analysis.- 1.2 On the Structure of this Book.- 1.3 About the Computer Programs.- 2 Probabilities.- 2.1 Experiments, Events, Sample Space.- 2.2 The Concept of Probability.- 2.3 Rules of Probability Calculus. Conditional Probability.- 2.4 Examples.- 2.4.1 Probability for n Dots in the Throwing of Two Dice.- 2.4.2 Lottery 6 out of 49.- 2.4.3 Three-Door Game.- 2.5 Problems.- 2.5.1 Determination of Probabilities through Symmetry Considerations.- 2.5.2 Probability for Non-exclusive Events.- 2.5.3 Dependent and Independent Events.- 2.5.4 Complementary Events.- 2.5.5 Probabilities Drawn from Large and Small Populations.- 2.6 Hints and Solutions.- 3 Random Variables. Distributions.- 3.1 Random Variables.- 3.2 Distributions of a Single Random Variable.- 3.3 Functions of a Single Random Variable, Expectation Value, Variance, Moments.- 3.4 Distribution Function and Probability Density of Two Variables. Conditional Probability.- 3.5 Expectation Values, Variance, Covariance, and Correlation.- 3.6 More than Two Variables. Vector and Matrix Notation.- 3.7 Transformation of Variables.- 3.8 Linear and Orthogonal Transformations. Error Propagation.- 3.9 Problems.- 3.9.1 Mean, Variance, and Skewness of a Discrete Distribution.- 3.9.2 Mean, Mode, Median, and Variance of a Continuous Distribution.- 3.9.3 Transformation of a Single Variable.- 3.9.4 Transformation of Several Variables.- 3.9.5 Error Propagation.- 3.9.6 Covariance and Correlation.- 3.10 Hints and Solutions.- 4 Computer Generated Random Numbers.The Monte Carlo Method.- 4.1 Random Numbers.- 4.2 Representation of Numbers in a Computer.- 4.3 Linear Congruential Generators.- 4.4 Multiplicative Linear Congruential Generators.- 4.5 Quality of an MLCG. Spectral Test.- 4.6 Implementation and Portability of an MLCG.- 4.7 Combination of Several MLCGs.- 4.8 Program for Generation of Uniformly Distributed Random Numbers.- 4.9 Generation of Arbitrarily Distributed Random Numbers.- 4.9.1 Generation by Transformation of the Uniform Distribution.- 4.9.2 Generation with the von Neumann Acceptance-Rejection Technique.- 4.10 Generation of Normally Distributed Random Numbers.- 4.11 Generation of Random Numbers According to a Multivariate Normal Distribution.- 4.12 The Monte Carlo Method for Integration.- 4.13 The Monte Carlo Method for Simulation.- 4.14 Example Programs.- 4.14.1 Main Program E1RN to Demonstrate Subprograms RNMLCG, RNECUY, and RNSTNR.- 4.14.2 Main Program E2RN to Demonstrate Subprogram RNLINE.- 4.14.3 Main Program E3RN to Demonstrate Subprogram RNRADI.- 4.14.4 Main Program E4RN to Simulate Molecular Movement of a Gas.- 4.14.5 Main Program E5RN to Demonstrate Subprograms RNMNPR and RNMNGN.- 4.15 Programming Problems.- 4.15.1 Program to Generate Breit-Wigner-Distributed Random Numbers.- 4.15.2 Program to Generate Random Numbers from a Triangular Distribution.- 4.15.3 Program to Generate Data Points with Errors of Different Size.- 4.15.4 Programs to Simulate Molecular Movement.- 5 Some Important Distributions and Theorems.- 5.1 The Binomial and Multinomial Distributions.- 5.2 Frequency. The Law of Large Numbers.- 5.3 The Hypergeometric Distribution.- 5.4 The Poisson Distribution.- 5.5 The Characteristic Function of a Distribution.- 5.6 The Standard Normal Distribution.- 5.7 The Normal or Gaussian Distribution.- 5.8 Quantitative Properties of the Normal Distribution.- 5.9 The Central Limit Theorem.- 5.10 The Multivariate Normal Distribution.- 5.11 Convolutions of Distributions.- 5.11.1 Folding Integrals.- 5.11.2 Convolutions with the Normal Distribution.- 5.12 Example Programs.- 5.12.1 Main Program E1DS to Simulate Empirical Frequency and Demonstrate Statistical Fluctuations.- 5.12.2 Main Program E2DS to Simulate the Experiment of Rutherford and Geiger.- 5.12.3 Main Program E3DS to Simulate Galton's Board.- 5.13 Problems.- 5.13.1 Binomial Distribution.- 5.13.2 Poisson Distribution.- 5.13.3 Normal Distribution.- 5.13.4 Multivariate Normal Distributi