How to generate bivariate random normally distributed 3d array?

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Nainsi Gupta
Nainsi Gupta 2023-5-31
评论： Nainsi Gupta 2023-6-1
Ran in:
mu= [0 0]
mu = 1×2
0 0
sigma= [1 0.25; .25 1]
sigma = 2×2
1.0000 0.2500 0.2500 1.0000
mvnrnd(mu,sigma,100)
ans = 100×2
0.7082 0.2195 -2.3244 -1.9734 -1.8774 0.1327 -0.2237 1.3953 -0.7603 0.4547 -1.2340 0.0526 0.8824 0.1801 0.1022 0.6385 -1.9730 -1.0128 1.3997 0.4401
I want to generate a 3-by-2-by-100 array which is normally distributed with given mu and sigma. Please help me how can I do this?
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John D'Errico
John D'Errico 2023-5-31
Since the realizations of such a random variable are i.i.d., it is sort of irrelevant what the 1st and third diemsnions mean!
Torsten
Torsten 2023-5-31
编辑：Torsten 2023-5-31
Yes, but don't you agree that for the k-dimensional case (see below), it's much more handy for access to have the realizations in a (n x k) matrix instead of a whatever matrix ?

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John D'Errico
John D'Errico 2023-5-31
编辑：John D'Errico 2023-5-31
Ran in:
Um, trivial?
You apparently want to generate 300 samples of a bivariate normal. So generate them as a 300x2 array, Then reshape and permute them into the desired 3x2x100 array.
mu= [0 0];
sigma= [1 0.25; .25 1];
X = mvnrnd(mu,sigma,300);
X = reshape(X,[3,100,2]);
X = permute(X,[1 3 2]);
size(X)
ans = 1×3
3 2 100
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John D'Errico
John D'Errico 2023-5-31
Ran in:
Permute is like transpose. But it applies to arrays of multiple dimensions.
Look at what I did.
mu= [0 0];
sigma= [1 0.25; .25 1];
X = mvnrnd(mu,sigma,300);
What is the initial size of X?
size(X)
ans = 1×2
300 2
I generated 300 samples of bivariate random numbers with the desired distribution. What did reshape do?
X = reshape(X,[3,100,2]);
size(X)
ans = 1×3
3 100 2
So I simply reshaped that into an array of 3x100 instances of the same random numbers. FInally, the call to permute does nothing more than transpose the second and third dimensions.
X = permute(X,[1 3 2]);
size(X)
ans = 1×3
3 2 100
Again, permute is just like transpose. It allows you to transpose any dimensions you wish. It applies to 3-d and higher dimension arrays.
You will do exactly the same thing, IF you wanted to generate trivariate random numbers. But now you will have a 3 instead of a 2 in those places in the reshape and permute.

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