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| Meta Title | Beta Distribution — Intuition, Examples, and Derivation | by Aerin Kim | TDS Archive | Medium |
| Meta Description | Beta Distribution — Intuition, Examples, and Derivation When should we use the Beta distribution? The Beta distribution is a probability distribution on probabilities. It is a versatile … |
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| Boilerpipe Text | When should we use the Beta distribution?
9 min read
Jan 8, 2020
--
The Beta distribution is
a probability distribution
on probabilities
.
It is a versatile probability distribution that could be used to model probabilities in different scenarios. Examples include the Click-Through Rate (CTR) of an advertisement, the conversion rate of customers purchasing on your website, the likelihood of readers clapping for your blog, the probability of Trump winning a second term, the 5-year survival rate for women with breast cancer, and so on.
Because the Beta distribution models a probability, its domain is bounded between
0
and
1
.
1. Why does the PDF for Beta distribution look the way it does?
To grasp the intuition behind the Beta distribution, let’s first examine its Probability Density Function (PDF):
Press enter or click to view image in full size
An excerpt from Wikipedia
What’s the intuition?
Ignoring
the coefficient
1/B(α,β)
for now, let’s focus on the numerator
x^(α-1) * (1-x)^(β-1).
Because the coefficient
1/B(α,β)
is just a normalizing constant, ensuring that the function integrates to 1.
Then, the terms in the numerator —
x to the power of something multiplied by 1-x to the power of
… |
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# Beta Distribution — Intuition, Examples, and Derivation
## When should we use the Beta distribution?
[](https://medium.com/@aerinykim?source=post_page---byline--cf00f4db57af---------------------------------------)
[Aerin Kim](https://medium.com/@aerinykim?source=post_page---byline--cf00f4db57af---------------------------------------)
9 min read
·
Jan 8, 2020
\--
24
Share
The Beta distribution is **a probability distribution *on probabilities***.
It is a versatile probability distribution that could be used to model probabilities in different scenarios. Examples include the Click-Through Rate (CTR) of an advertisement, the conversion rate of customers purchasing on your website, the likelihood of readers clapping for your blog, the probability of Trump winning a second term, the 5-year survival rate for women with breast cancer, and so on.
Because the Beta distribution models a probability, its domain is bounded between **0** and **1**.
## 1\. Why does the PDF for Beta distribution look the way it does?
To grasp the intuition behind the Beta distribution, let’s first examine its Probability Density Function (PDF):
Press enter or click to view image in full size
![]()
An excerpt from Wikipedia
### What’s the intuition?
**Ignoring** **the coefficient** **1/B(α,β)** for now, let’s focus on the numerator **x^(α-1) \* (1-x)^(β-1).** Because the coefficient **1/B(α,β)** is just a normalizing constant, ensuring that the function integrates to 1.
Then, the terms in the numerator — **x to the power of something multiplied by 1-x to the power of**…
\--
\--
24
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| Readable Markdown | ## When should we use the Beta distribution?
[](https://medium.com/@aerinykim?source=post_page---byline--cf00f4db57af---------------------------------------)
9 min read Jan 8, 2020
\--
The Beta distribution is **a probability distribution *on probabilities***.
It is a versatile probability distribution that could be used to model probabilities in different scenarios. Examples include the Click-Through Rate (CTR) of an advertisement, the conversion rate of customers purchasing on your website, the likelihood of readers clapping for your blog, the probability of Trump winning a second term, the 5-year survival rate for women with breast cancer, and so on.
Because the Beta distribution models a probability, its domain is bounded between **0** and **1**.
## 1\. Why does the PDF for Beta distribution look the way it does?
To grasp the intuition behind the Beta distribution, let’s first examine its Probability Density Function (PDF):
Press enter or click to view image in full size
An excerpt from Wikipedia
### What’s the intuition?
**Ignoring** **the coefficient** **1/B(α,β)** for now, let’s focus on the numerator **x^(α-1) \* (1-x)^(β-1).** Because the coefficient **1/B(α,β)** is just a normalizing constant, ensuring that the function integrates to 1.
Then, the terms in the numerator — **x to the power of something multiplied by 1-x to the power of**… |
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