Overview of this book

Simulation modeling helps you to create digital prototypes of physical models to analyze how they work and predict their performance in the real world. With this comprehensive guide, you'll understand various computational statistical simulations using Python. Starting with the fundamentals of simulation modeling, you'll understand concepts such as randomness and explore data generating processes, resampling methods, and bootstrapping techniques. You'll then cover key algorithms such as Monte Carlo simulations and Markov decision processes, which are used to develop numerical simulation models, and discover how they can be used to solve real-world problems. As you advance, you'll develop simulation models to help you get accurate results and enhance decision-making processes. Using optimization techniques, you'll learn to modify the performance of a model to improve results and make optimal use of resources. The book will guide you in creating a digital prototype using practical use cases for financial engineering, prototyping project management to improve planning, and simulating physical phenomena using neural networks. By the end of this book, you'll have learned how to construct and deploy simulation models of your own to overcome real-world challenges.
Preface
Section 1: Getting Started with Numerical Simulation
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Chapter 1: Introducing Simulation Models
Chapter 2: Understanding Randomness and Random Numbers
Chapter 3: Probability and Data Generation Processes
Section 2: Simulation Modeling Algorithms and Techniques
Chapter 4: Exploring Monte Carlo Simulations
Chapter 5: Simulation-Based Markov Decision Processes
Chapter 6: Resampling Methods
Chapter 7: Using Simulation to Improve and Optimize Systems
Section 3: Real-World Applications
Chapter 8: Using Simulation Models for Financial Engineering
Chapter 9: Simulating Physical Phenomena Using Neural Networks
Chapter 10: Modeling and Simulation for Project Management
Chapter 11: What's Next?
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Test adaptation (that is, the goodness of fit) in general, has the purpose of verifying whether a variable under examination does or does not have a certain hypothesized distribution on the basis, as usual, of experimental data. It is used to compare a set of frequencies observed in a sample, with similar theoretical quantities assumed for the population. By means of the test, it is possible to quantitatively measure the degree of deviation between the two sets of values.

The results obtained in the samples do not always exactly agree with the theoretical results that are expected according to the rules of probability. Indeed, it is very rare for this to occur. For example, although theoretical considerations lead us to expect 100 heads and 100 tails from 200 flips of a coin, it is rare that these results are obtained exactly. However, despite this, we must not unnecessarily deduce that the coin is rigged.

The chi-squared test

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