# Generate random variate: What does this symbol mean?

#### tsukiko

##### New Member
Hi.
I'm reading a book about how to simulate random variate (from some distribution).
But, when i look at the algorithm there, is has a leftarrow symbol, which i'm not sure what does it mean. I try googling but most of the results only state the LaTeX code for such symbol without further explanation. If someone does know the meaning of that leftarrow symbol, please tell me. Thanks in advanced.

P/S: Sorry if this is not the right place to ask such a general question. But since i came across it when reading a book on simulation and i'm using R for my programming, i think this is the best place to ask.

#### Dason

... we'll definitely need more context or a picture or something to be able to offer any help.

#### tsukiko

##### New Member
Ok, let say we use the inverse transform method to generate the random variate from continuous distribution. So, the algorithm to do so is given as follows:
1. Generate U from U(0,1).
2. X \leftarrow F_{x}^{-1}(U)
3. Deliver X.

In this context, i believe the \leftarrow means equal i.e. we let X equal inverse function of U.

But, for a further example, i'm not sure if the \leftarrow use in this book (there is no notation section for the book anyway) really mean equal. Let's look at the following example of generating random variate from discrete variable using (still) the inverse transform method:

1.C \leftarrow P_0
2.B \leftarrow C
3.K \leftarrow 0
4.Generate U from U(0,1)
5.If U<=B (U<=g_k), deliver X=x_k
6.K \leftarrow K+1
7.C \leftarrow A_{k+1}C (P_{k+1}=A_{k+1}P_k)
8.B \leftarrow B+C (g_{k+1}=g_k+P{k+1})
9.Go to step 5.

I guess the leftarrow in all these means equal, but rather than using the usual equal sign i.e. '=' , we use the \leftarrow symbol to denote that this value keep changing due to the looping process executed here. That's my assumption. Please advise me if there is any reference about the symbol meaning here i.e. please let me know if there is any 'global' / general meaning to this symbol. I'm a little bit confused since this is my first time seeing this \leftarrow symbol.

#### trinker

##### ggplot2orBust
Yes this essentially means equal and in most cases works the same. The <- operator is an assignment operator that is generally good practice when assigning values to objects. This is an old coding convention (not new or unique to R) left over from when keyboards actually contained a single key to make <-.

#### Dason

Does the book use R? <- is used for assignment in R (and a few other languages) so that would make sense.

#### tsukiko

##### New Member
Ok, i think i'm not using a clear notation. What i'm trying to type is the attachment.
Hope that will be clear. And the left arrow i'm talking about is the one in the attachment.
What does it mean? i guess it is an equal sign.

@Dason: the book didnt use R. and the one i attach is just an algorithm not any codes of any language including R. but i'm going to make some simulation with R. sorry again if this is not the right place to ask about the symbol, still i'm hoping someone can give some explanation on what does the leftarrow symbol mean.

#### Dason

I believe they're just using it in an algorithmic sense to mean "assign to". So $$C \leftarrow P_0$$ just means assign the "C" the value of $$P_0 = P(X = 0)$$