#### Overview of this book

Today's world of science and technology is all about speed and flexibility. When it comes to scientific computing, NumPy is on the top of the list. NumPy will give you both speed and high productivity. "NumPy Cookbook" will teach you all about NumPy, a leading scientific computing library. NumPy replaces a lot of the functionality of Matlab and Mathematica, but in contrast to those products, it is free and open source. "Numpy Cookbook" will teach you to write readable, efficient, and fast code that is as close to the language of Mathematics as much as possible with the cutting edge open source NumPy software library. You will learn about installing and using NumPy and related concepts. At the end of the book, we will explore related scientific computing projects. This book will give you a solid foundation in NumPy arrays and universal functions. You will also learn about plotting with Matplotlib and the related SciPy project through examples. "NumPy Cookbook" will help you to be productive with NumPy and write clean and fast code.
NumPy Cookbook
Credits
www.PacktPub.com
Preface
Free Chapter
Winding Along with IPython
Get to Grips with Commonly Used Functions
Connecting NumPy with the Rest of the World
Audio and Image Processing
Special Arrays and Universal Functions
Profiling and Debugging
Quality Assurance
Speed Up Code with Cython
Index

## Discovering a power law

For the purpose of this recipe, imagine that we are operating a Hedge Fund. Let it sink in; you are part of the one percent now!

Power laws occur in a lot of places, see `http://en.wikipedia.org/wiki/Power_law` for more information. The Pareto principle (http://en.wikipedia.org/wiki/Pareto_principle) for instance, which is a power law, states that wealth is unevenly distributed. This principle tells us that if we group people by their wealth, the size of the groups will vary exponentially. To put it simply, there are not a lot of rich people, and there are even less billionaires; hence the one percent.

Assume that there is a power law in the closing stock prices log returns. This is a big assumption, of course, but power law assumptions seem to pop up all over the place.

We don't want to trade too often, because of involved transaction costs per trade. Let's say that we would prefer to buy and sell once a month based on a significant correction (in other words a big drop...