Book Image

Building Statistical Models in Python

By : Huy Hoang Nguyen, Paul N Adams, Stuart J Miller
Book Image

Building Statistical Models in Python

By: Huy Hoang Nguyen, Paul N Adams, Stuart J Miller

Overview of this book

The ability to proficiently perform statistical modeling is a fundamental skill for data scientists and essential for businesses reliant on data insights. Building Statistical Models with Python is a comprehensive guide that will empower you to leverage mathematical and statistical principles in data assessment, understanding, and inference generation. This book not only equips you with skills to navigate the complexities of statistical modeling, but also provides practical guidance for immediate implementation through illustrative examples. Through emphasis on application and code examples, you’ll understand the concepts while gaining hands-on experience. With the help of Python and its essential libraries, you’ll explore key statistical models, including hypothesis testing, regression, time series analysis, classification, and more. By the end of this book, you’ll gain fluency in statistical modeling while harnessing the full potential of Python's rich ecosystem for data analysis.
Table of Contents (22 chapters)
1
Part 1:Introduction to Statistics
7
Part 2:Regression Models
10
Part 3:Classification Models
13
Part 4:Time Series Models
17
Part 5:Survival Analysis

Exponential model

In the last section, we studied the non-parametric Kaplan-Meier survival model. We will now bridge parametric modeling with the exponential model and then will discuss a semi-parametric model, the Cox Proportional Hazards model, in the next section. Before considering the exponential model, we will review what the exponential distribution is and why we mention it in this section. This distribution is based on the Poisson process. Here, events occur independently over time and the event rate, λ, is calculated by the number of occurrences per unit of time, as follows:

λ = Y _ t 

The Poisson distribution is a statistical discrete distribution concerning the number of events occurring in a specified time period. It is defined as follows. Let Y be the number of occurrences in time t. Y follows the Poisson distribution with parameter λ if a probability mass function is given by the following formula:

f(Y) = Pr(y = Y) = e ...