Efnisyfirlit

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• 1. Introduction and Overview
  • 1.1 Making decisions under uncertainty
  • 1.2 Overview of this book
  • Summary and conclusions
  • Exercises
• Part I: Probability and Random Variables
  • 2. Probability
    • 2.1 Events and their probabilities
      • 2.1.1 Outcomes, events, and the sample space
      • 2.1.2 Set operations
    • 2.2 Rules of Probability
      • 2.2.1 Axioms of Probability
      • 2.2.2 Computing probabilities of events
      • 2.2.3 Applications in reliability
    • 2.3 Combinatorics
      • 2.3.1 Equally likely outcomes
      • 2.3.2 Permutations and combinations
    • 2.4 Conditional probability and independence
    • Summary and conclusions
    • Exercises
  • 3. Discrete Random Variables and Their Distributions
    • 3.1 Distribution of a random variable
      • 3.1.1 Main concepts
      • 3.1.2 Types of random variables
    • 3.2 Distribution of a random vector
      • 3.2.1 Joint distribution and marginal distributions
      • 3.2.2 Independence of random variables
    • 3.3 Expectation and variance
      • 3.3.1 Expectation
      • 3.3.2 Expectation of a function
      • 3.3.3 Properties
      • 3.3.4 Variance and standard deviation
      • 3.3.5 Covariance and correlation
      • 3.3.6 Properties
      • 3.3.7 Chebyshev’s inequality
      • 3.3.8 Application to finance
    • 3.4 Families of discrete distributions
      • 3.4.1 Bernoulli distribution
      • 3.4.2 Binomial distribution
      • 3.4.3 Geometric distribution
      • 3.4.4 Negative Binomial distribution
      • 3.4.5 Poisson distribution
      • 3.4.6 Poisson approximation of Binomial distribution
      • Summary and conclusions
      • Exercises
  • 4. Continuous Distributions
    • 4.1 Probability density
    • 4.2 Families of continuous distributions
      • 4.2.1 Uniform distribution
      • 4.2.2 Exponential distribution
      • 4.2.3 Gamma distribution
      • 4.2.4 Normal distribution
    • 4.3 Central Limit Theorem
    • Summary and conclusions
    • Exercises
  • 5. Computer Simulations and Monte Carlo Methods
    • 5.1 Introduction
      • 5.1.1 Applications and examples
    • 5.2 Simulation of random variables
      • 5.2.1 Random number generators
      • 5.2.2 Discrete methods
      • 5.2.3 Inverse transform method
      • 5.2.4 Rejection method
      • 5.2.5 Generation of random vectors
      • 5.2.6 Special methods
    • 5.3 Solving problems by Monte Carlo methods
      • 5.3.1 Estimating probabilities
      • 5.3.2 Estimating means and standard deviations
      • 5.3.3 Forecasting
      • 5.3.4 Estimating lengths, areas, and volumes
      • 5.3.5 Monte Carlo integration
      • Summary and conclusions
      • Exercises
• Part II: Stochastic Processes
  • 6. Stochastic Processes
    • 6.1 Definitions and classifications
    • 6.2 Markov processes and Markov chains
      • 6.2.1 Markov chains
      • 6.2.2 Matrix approach
      • 6.2.3 Steady-state distribution
    • 6.3 Counting processes
      • 6.3.1 Binomial process
      • 6.3.2 Poisson process
    • 6.4 Simulation of stochastic processes
    • Summary and conclusions
    • Exercises
  • 7. Queuing Systems
    • 7.1 Main components of a queuing system
    • 7.2 The Little’s Law
    • 7.3 Bernoulli single-server queuing process
      • 7.3.1 Systems with limited capacity
    • 7.4 M/M/1 system
      • 7.4.1 Evaluating the system’s performance
    • 7.5 Multiserver queuing systems
      • 7.5.1 Bernoulli k-server queuing process
      • 7.5.2 M/M/k systems
      • 7.5.3 Unlimited number of servers and M/M/∞
    • 7.6 Simulation of queuing systems
    • Summary and conclusions
    • Exercises
• Part III: Statistics
  • 8. Introduction to Statistics
    • 8.1 Population and sample, parameters and statistics
    • 8.2 Descriptive statistics
      • 8.2.1 Mean
      • 8.2.2 Median
      • 8.2.3 Quantiles, percentiles, and quartiles
      • 8.2.4 Variance and standard deviation
      • 8.2.5 Standard errors of estimates
      • 8.2.6 Interquartile range
    • 8.3 Graphical statistics
      • 8.3.1 Histogram
      • 8.3.2 Stem-and-leaf plot
      • 8.3.3 Boxplot
      • 8.3.4 Scatter plots and time plots
      • Summary and conclusions
      • Exercises
  • 9. Statistical Inference I
    • 9.1 Parameter estimation
      • 9.1.1 Method of moments
      • 9.1.2 Method of maximum likelihood
      • 9.1.3 Estimation of standard errors
    • 9.2 Confidence intervals
      • 9.2.1 Construction of confidence intervals: a general method
      • 9.2.2 Confidence interval for the population mean
      • 9.2.3 Confidence interval for the difference between two means
      • 9.2.4 Selection of a sample size
      • 9.2.5 Estimating means with a given precision
    • 9.3 Unknown standard deviation
      • 9.3.1 Large samples
      • 9.3.2 Confidence intervals for proportions
      • 9.3.3 Estimating proportions with a given precision
      • 9.3.4 Small samples: Student’s t distribution
      • 9.3.5 Comparison of two populations with unknown variances
    • 9.4 Hypothesis testing
      • 9.4.1 Hypothesis and alternative
      • 9.4.2 Type I and Type II errors: level of significance
      • 9.4.3 Level α tests: general approach
      • 9.4.4 Rejection regions and power
      • 9.4.5 Standard Normal null distribution (Z-test)
      • 9.4.6 Z-tests for means and proportions
      • 9.4.7 Pooled sample proportion
      • 9.4.8 Unknown σ: T-tests
      • 9.4.9 Duality: two-sided tests and two-sided confidence intervals
      • 9.4.10 P-value
    • 9.5 Inference about variances
      • 9.5.1 Variance estimator and Chi-square distribution
      • 9.5.2 Confidence interval for the population variance
      • 9.5.3 Testing variance
      • 9.5.4 Comparison of two variances. F-distribution
      • 9.5.5 Confidence interval for the ratio of population variances
      • 9.5.6 F-tests comparing two variances
      • Summary and conclusions
      • Exercises
  • 10. Statistical Inference II
    • 10.1 Chi-square tests
      • 10.1.1 Testing a distribution
      • 10.1.2 Testing a family of distributions
      • 10.1.3 Testing independence
    • 10.2 Nonparametric statistics
      • 10.2.1 Sign test
      • 10.2.2 Wilcoxon signed rank test
      • 10.2.3 Mann–Whitney–Wilcoxon rank sum test
    • 10.3 Bootstrap
      • 10.3.1 Bootstrap distribution and all bootstrap samples
      • 10.3.2 Computer generated bootstrap samples
      • 10.3.3 Bootstrap confidence intervals
    • 10.4 Bayesian inference
      • 10.4.1 Prior and posterior
      • 10.4.2 Bayesian estimation
      • 10.4.3 Bayesian credible sets
      • 10.4.4 Bayesian hypothesis testing
      • Summary and conclusions
      • Exercises
  • 11. Regression
    • 11.1 Least squares estimation
      • 11.1.1 Examples
      • 11.1.2 Method of least squares
      • 11.1.3 Linear regression
      • 11.1.4 Regression and correlation
      • 11.1.5 Overfitting a model
    • 11.2 Analysis of variance, prediction, and further inference
      • 11.2.1 ANOVA and R-square
      • 11.2.2 Tests and confidence intervals
      • 11.2.3 Prediction
    • 11.3 Multivariate regression
      • 11.3.1 Introduction and examples
      • 11.3.2 Matrix approach and least squares estimation
      • 11.3.3 Analysis of variance, tests, and prediction
    • 11.4 Model building
      • 11.4.1 Adjusted R-square
      • 11.4.2 Extra sum of squares, partial F-tests, and variable selection
      • 11.4.3 Categorical predictors and dummy variables
      • Summary and conclusions
      • Exercises
• Appendix
  • A.1 Data sets
  • A.2 Inventory of distributions
    • A.2.1 Discrete families
    • A.2.2 Continuous families
  • A.3 Distribution tables
  • A.4 Calculus review
    • A.4.1 Inverse function
    • A.4.2 Limits and continuity
    • A.4.3 Sequences and series
    • A.4.4 Derivatives, minimum, and maximum
    • A.4.5 Integrals
  • A.5 Matrices and linear systems
  • A.6 Answers to selected Exercises
• Index

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