#### 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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# Exploring the Jackknife technique

This method is used to estimate characteristics such as the distortion and the standard deviation of a statistic. This technique allows us to obtain the desired estimates without necessarily resorting to parametric assumptions. Jackknife is based on calculating the statistics of interest for the sub-samples we've obtained, leaving out one sample observation at a time. The jackknife estimate is consistent for various sample statistics, such as mean, variance, correlation coefficient, maximum likelihood estimator, and others.

## Defining the Jackknife method

The Jackknife method was proposed in 1949 by M. H. Quenouille who, due to the low computational power of the time, created an algorithm that requires a fixed number of accounts.

Important Note

The main idea behind this method is to cut a different observation from the original sample each time and to re-evaluate the parameter of interest. The estimate will be compared with the same...