How to retrieve the list of numbers from which the average of a normal simulation is derived?

Hello all!

I am currently using the following code to calculate the average of 5000 numbers simulated with a normal distribution with a changing mean and std deviation, from 75 to 125 and 1 to 40, respectively.

n = 5000; %Number of Simulations, sample size 
x1 = 75:125;  %Mean simulation range 
y1 = 1:40; %Standard Deviation range 
for i = 1:length(x1) % mean
    for j = 1:length(y1) % sd
    Exp_Pw(i,j) = mean(0.5*(normrnd(x1(i),y1(j),n,1)));    
    end   
end

The problem is that I don't know precisely the 5000 numbers where the average comes from, and I would like to have that information in maybe a cell array? (if this is the name) that would allow me to use those different simulated numbers in other operations. Any idea how to do it?

Thank you very much!

Answer 1

[David Hill]

n = 5000; %Number of Simulations, sample size 
x1 = 75:125;  %Mean simulation range 
y1 = 1:40; %Standard Deviation range 
N=zeros(n,length(y1),length(x1));
for i = 1:length(x1) % mean
    for j = 1:length(y1) % sd
        N(:,i,j)=normrnd(x1(i),y1(j),n,1);%this will contain all values
        Exp_Pw(i,j) = mean(0.5*(N(n,i,j)));    
    end   
end

[Angelavtc]

Thank you very much @David Hill! and how can I call this matrix element by element to generate other operations, for example, to calculate the variance of each simulation? I tried this code, but the dimensions are not correct.

for i = 1:length(x1) 
    for j = 1:length(y1)
        for r= 1:n
        Variance(i,j)=var(N(r,i,j));
    end
    end
end

[Jeff Miller]

for i = 1:length(x1) 
    for j = 1:length(y1)
        theseN = squeeze(N(:,i,j));
        Variance(i,j)=var(theseN);
    end
end

[Image Analyst]

@Angelavtc, when you say "How to retrieve the list of numbers from which the average of a normal simulation is derived?", that implies you have the average, but, for some reason, you don't have the "list of numbers" and you want to "retrieve" them from somewhere. So I have a question: How did you get the mean if you didn't have the numbers already and need to retrieve them? Did you just specify the mean arbitrarily and now want numbers that will have that mean?

[Angelavtc]

@Image Analyst yes, I told Matlab to create 5000 random numbers from a normal distribution with an specific mean and std (which was changing according to i and j). From those random numbers I got the mean... however, given the way the for loop was constructed, I was not able to identify the list of numbers. I was lacking the third dimension considered in the matrix, and now is clear. Thank you Matlab community!

[Image Analyst]

Since you can do

r = normrnd(mu,sigma)

you have r. I think the confusion was when you said you need to "retrieve" or "identify" r, when in fact you already had r.

I think what you really meant was that you wanted to save all the r into an array. And to save them (instead of just generating, using, and then throwing away the numbers inside each iteration, which would be fine by the way), then yes, you'd need a 3-D array to save them. Anyway, thanks for accepting David's answer to award him reputation points.

[Angelavtc]

yes @Image Analyst you are right, there was a mistake in the way I wrote my question. "Save" is better than "retrieve". Thank you!

Answer 2

[Image Analyst]

I'm not sure what you're asking. If all you have is a mean, say 75, then there are an infinite number of data values that could have gone into getting that mean of 75. You can't know them if all you have is the mean and standard deviation, though you could create some similar ones with randn().