<p>It means that <span class="math-container">$z$</span> has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector <span class="math-container">$z$</span> has a standard normal distribution.</p>

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2021-01-10T15:52:51.743Z
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nbro
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2020-08-23T19:19:47.283Z
2020-08-23T19:19:47.283Z
David
<p>I know that the notation <span class="math-container">$\mathcal{N}(\mu, \sigma)$</span> stands for a normal distribution.
But I'm reading the book &quot;An Introduction to Variational Autoencoders&quot; and in it, there is this notation:
<span class="math-container">$$\mathcal{N}(z; 0, I)$$</span>
What does it mean?</p>
<p>picture of the book:
<a href="https://i.sstatic.net/34JES.png" rel="noreferrer"><img src="https://i.sstatic.net/34JES.png" alt="picture of the book An Introduction to Variational Autoencoders" /></a></p>

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2021-01-10T15:54:21.857Z
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nbro
<terminology><variational-autoencoder><notation><random-variable><bayesian-statistics>
What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?
Peyman
# What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?

(Asked by: username_0 on 2020-08-23)

I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution.
But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation:
$$\mathcal{N}(z; 0, I)$$
What does it mean?

picture of the book:
[![picture of the book An Introduction to Variational Autoencoders](https://i.sstatic.net/34JES.png)](https://i.sstatic.net/34JES.png)

**Tags:** terminology, variational-autoencoder, notation, random-variable, bayesian-statistics

> **Comments:**
> **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/118284/discussion-on-question-by-peyman-what-does-the-notation-mathcalnz-mu-si).  

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## 1 answers

### Answer by username_2 on 2020-08-23. Score: 7 | Accepted answer

It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal distribution.

> **Comments:**
> **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/118283/discussion-on-answer-by-david-ireland-what-does-the-notation-mathcalnz-mu).  

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