MATLAB for uniform random variables

electroissues

1. The problem statement, all variables and given/known data

Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g = (x,y) = sqrt (-2ln(x) . cos(2piy). Since finding the distribution of g(X,Y) analytically is quite tough, I need to generate MATLAB program for

1 - 10,000 uniformly distributed random samples for X and Y
2 - For each sample of X and Y, compute Z= g(X,Y)
3 - Draw a histogram over the resulting samples in Z
4 - Estimate the moments mZ for n = 1,2....6.




3. The attempt at a solution

I tried for the first solution and I'm hopelessly stuck. MATLAB gives me an error saying "Attempted to access (0,1); index must be a positive integer or logical."

I don't understand where I'm going wrong.

Please help!

jbunniii

Please post exactly what Matlab command you have typed which produces that error.

electroissues

I tried to put the formula into MATLAB and this was my program

x= 0;
>> y= 1;
>> rand (1, 1000);
>> g= sqrt((-2*log(x)) * cos((2*pi*y)));
>> plot(g)

Actually, for this, I get a blank plot.
Please point out the mistake.

Mark44

Your error message came from an attempt to access the (0, 1) element of a an array.

Before starting to code, you should take a look at the Matlab documentation to learn how to use such functions as rand, log, and plot. In the code you show, x is 0, and your fourth line is attempting to take the log of 0

Getting started with MATLAB
User documentation

I can't really give you much help, since your code is a VERY LONG way from doing what you need it to do.

electroissues

Thanks for your comments but I need to point out thats the question in the first place. So there is no chance I can take a different value.

How do you suggest I define the vectors then? One of the vector (x) is multiplied with the log and the second vector (y) is multiplied with cos (2pi). And the question says X (note the upper case) = U (0,1)

Mark44

In your first post you said that X is uniformly distributed in [0, 1]. Below, you have changed that to say that X is uniformly distributed in (0, 1). The first interval includes 0 (and 1, but that's not a problem); the second interval doesn't include 0.
NO, it's NOT "multiplied with log" and NO, it's NOT "multiplied with cos (2pi)." These are functions, not numbers that you multiply by.
You can define your vectors X and Y as one-dimensional arrays with 10,000 elements or as two-dimensional arrays with 100 rows and 100 columns. It doesn't make any difference, but you need to learn how to work with vectors and/or arrays in MATLAB. The first link I gave in my earlier post can show you how to work with arrays.

electroissues

Thanks, Mark. I read the documentation.

In my first post, the question has U= [0,1] with 10,000 random variables.

Can you please tell me how I shud use this in the rand function? Also, please help with the substitution for x and y if I define the rand as "rand [1, 10000]"

Thanks again.

Mark44

Yes, I'm aware of what you had in your first post. My comment was that in post #5 you said U(0, 1), so which is it?
Here's from the documentation for rand: "r = rand(n) returns an n-by-n matrix containing pseudorandom values drawn from the standard uniform distribution on the open interval (0,1). rand(m,n) or rand([m,n]) returns an m-by-n matrix."

You can do this to create a 100 x 100 array of random numbers in the open interval (0, 1):
X = rand(100)

Or you can do this to create a vector of length 10000 of numbers from the same interval:
X = rand(1, 10000)

Whatever you do to create your X array, do the same to create the Y array.