#### Overview of this book

Data Science with R aims to teach you how to begin performing data science tasks by taking advantage of Rs powerful ecosystem of packages. R being the most widely used programming language when used with data science can be a powerful combination to solve complexities involved with varied data sets in the real world. The book will provide a computational and methodological framework for statistical simulation to the users. Through this book, you will get in grips with the software environment R. After getting to know the background of popular methods in the area of computational statistics, you will see some applications in R to better understand the methods as well as gaining experience of working with real-world data and real-world problems. This book helps uncover the large-scale patterns in complex systems where interdependencies and variation are critical. An effective simulation is driven by data generating processes that accurately reflect real physical populations. You will learn how to plan and structure a simulation project to aid in the decision-making process as well as the presentation of results. By the end of this book, you reader will get in touch with the software environment R. After getting background on popular methods in the area, you will see applications in R to better understand the methods as well as to gain experience when working on real-world data and real-world problems.
Simulation for Data Science with R
Credits
www.PacktPub.com
Preface
Free Chapter
Introduction
R and High-Performance Computing
The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions
Simulation of Random Numbers
Monte Carlo Methods for Optimization Problems
Probability Theory Shown by Simulation
Resampling Methods
Applications of Resampling Methods and Monte Carlo Tests
The EM Algorithm
Simulation with Complex Data
System Dynamics and Agent-Based Models
Index

## Simulation of non-uniform distributed random variables

So far, the simulation of the same random variable was discussed. In fact, the generation of uniform random numbers is a very important step. The methods for generating non-uniform random numbers are different. The main aim is to transform random numbers from a uniform distribution to another distribution. Generally, a uniformly distributed random variable, can accordingly be transformed and modified to obtain other distributions.

### The inversion method

The condition is that uniformly distributed random numbers are already generated in the interval [0,1]. The inversion method takes advantage of the fact that a distribution function is also defined in the interval [0,1].

Let be the distribution function of V. Through the plug-in of a uniform random number into the inverse distribution function

, we get a random number with the distribution V.

A prerequisite for the application of an inversion process is therefore the existence of the analytic...