Book Image

Java Data Analysis

By : John R. Hubbard
Book Image

Java Data Analysis

By: John R. Hubbard

Overview of this book

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the aim of discovering useful information. Java is one of the most popular languages to perform your data analysis tasks. This book will help you learn the tools and techniques in Java to conduct data analysis without any hassle. After getting a quick overview of what data science is and the steps involved in the process, you’ll learn the statistical data analysis techniques and implement them using the popular Java APIs and libraries. Through practical examples, you will also learn the machine learning concepts such as classification and regression. In the process, you’ll familiarize yourself with tools such as Rapidminer and WEKA and see how these Java-based tools can be used effectively for analysis. You will also learn how to analyze text and other types of multimedia. Learn to work with relational, NoSQL, and time-series data. This book will also show you how you can utilize different Java-based libraries to create insightful and easy to understand plots and graphs. By the end of this book, you will have a solid understanding of the various data analysis techniques, and how to implement them using Java.
Table of Contents (20 chapters)
Java Data Analysis
Credits
About the Author
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
Index

The central limit theorem


A random sample is a set of numbers S = {x1, x2,... , xn}, each of which is a measurement of some unknown value that we seek. We can assume that each xi is a value of a random variable Xi, and that all these random variables X1, X2,…, Xn are independent and have the same distribution with mean μ and standard deviation σ. Let Sn and Z be the random variables:

The central limit theorem states that the random variable Z tends to be normally distributed as n gets larger. That means that the PDF of Z will be close to the function φ(x) and the larger n is, the closer it will be.

By dividing numerator and denominator by n, we have this alternative formula for Z:

This isn't any simpler. But if we designate the random variable as:

then we can write Z as:

The central limit theorem tells us that this standardization of the random variable is nearly distributed as the standard normal distribution φ(x). So, if we take n measurements x1, x2,…, xn of an unknown quantity that has...