The Normal Distribution vs. Student’s T-Distribution

An intuitive visualization of why we use t-distributions

Introduction

The Normal Distribution

The generic form probability density function for a normal distribution
The generic form probability density function for a normal distribution
The probability density function for a normal distribution

Code:

Explanation:

Output:

Student’s T-Distribution

The probability density function for Student’s t-distribution
The probability density function for Student’s t-distribution
The probability density function for Student’s t-distribution

Code:

Explanation:

Output:

A graph of Student’s t-distribution with a single degree of freedom
A graph of Student’s t-distribution with a single degree of freedom

A Visual Comparison

Code:

Output:

A graph comparing the standard normal distribution to a t-distribution with one degree of freedom
A graph comparing the standard normal distribution to a t-distribution with one degree of freedom

Key Differences:

An animated gif showing a t-distribution vs the normal distribution for degrees of freedom ranging from 1 to 50
An animated gif showing a t-distribution vs the normal distribution for degrees of freedom ranging from 1 to 50

Conclusion

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Software Engineer at Rhove. Former Investment Specialist for a private wealth management firm.