Notation for number of draws from a distribution

Question

I know that we specify a draw from a distribution as

$$x\sim N(0,1)$$

but what is the notation for specifying the number of samples from the distribution. In other words how would notation clarify the difference between

rnorm(mean=0,sd=1,n=10)

vs

rnorm(mean=0,sd=1,n=50)

Matthew Drury · Accepted Answer · 2017-08-15 05:46:18Z

3

I do this:

$$x_1, x_2, ..., x_{50} \sim N(0, 1)$$

and then mention independence in the prose - no need for notation to communicate that part.

answered Aug 15, 2017 at 5:38

Matthew Drury

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2

$\begingroup$ This is good -- however, notation can communicate independence, for example $X_i \stackrel{\text{iid}}{\sim} N(0, 1),\, i=1,2,...,50$ $\endgroup$
– Glen_b
Commented Aug 15, 2017 at 6:16
$\begingroup$ I thought of something similar, but it bothered me a little that the i.d. part is extraneous. $\endgroup$
– Matthew Drury
Commented Aug 15, 2017 at 6:22
$\begingroup$ @MatthewDrury why not specify the dimensions? $x\sim N(0,1)$ where $x \in R^{50}$. This seems to be clear in specifying how long a vector is. This way you can have $x_i \sim N(0,1)$ where $i=1,\dots,3$ and $x_1 \in R^{10}$, $x_2 \in R^{100}$, and $x_3 \in R^{1000}$. This makes it clear that three samples a being drawn, each having a different number of draws. $\endgroup$
– Alex
Commented Aug 15, 2017 at 15:53
2

$\begingroup$ Of course you can. I suppose that I have this general opinion, and it is an opinion, that notation should only be used when it is clarifying. It's the kind of thing to me that is best used in moderation. I tend to use more text and words than other math/stats communicators, because that's more clear to me. $\endgroup$
– Matthew Drury
Commented Aug 15, 2017 at 18:59

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