Question re-asking: cdfMvne and multivariate logistic function

Hello Aptech:

I am sorry for keeping asking the similar questions. The following is my questions based on my previous post here.

Q1:

In the first post I made, "How to obtain mutivariate normal distribution with mean u and covariance matrix using cdfMvn", you introduced to me the use of "cdfMvne. The example we did last time is that, for a two-dimention random vector Z=[Z1,Z2], if they are evaluated at [z1, z2] such as:

//Upper limits of integration
ulim = { -0.5, 1 };

with non-zero mean vector

mu = { 0.76, 1.1 };

and Correlation matrix

corr = { 1 0.26, 0.26 1 };

then the solution given last time is to use the command

{ p2, tol, err } = cdfMvne(cdfmControlCreate(), ulim_t, corr, mu_t);
print p2;

However, I have two problems as follows: 1) ulim_t and mu_t are not defined, which I believe they should be ulim and mu defined above. 2) the results from print p2 gives

0.10383468
0.59483487

which is not 0.066579035 from the command :

cdfMvn(ulim-mu, corr)

I understand that if corr is a (2 by 2) diagonal matrix, then I simply multiply the number from p2 to get the joint density P(Z1<z1, Z2<z2). My question now is how should I get the joint density P(Z1<z1, Z2<z2) from cdfMvne() when the correlation matrix is not diagonal?

Q2:

This question is to ask how should I compute in GAUSS a multivariate logistic function with non-zero mean and non-diagonal correlation matrix?

Thank you very much for your help as always!

1 Answer

0

accepted

There is no reason to apologize for asking questions. That is the purpose of the forum. 🙂

Regarding Q1

I think all of your problems are coming because cdfMVne requires the integration limits and mean to be a ROW vector, while cdfMVn takes in COLUMN vectors. Here is an example that does what you want

//No commas between elements
//so they are row vectors
ulim = { 0 0 };
mu = { 0 0 };

//Non-diagonal correlation matrix
corr = {    1    0.26,
         0.26       1 };

//Declare 'ctl' to be a cdfmControl struct
//and fill with default settings
struct cdfmControl ctl;
ctl = cdfmControlCreate();

{ p2, a, b } = cdfMVne(ctl,ulim, corr,mu);
print p2;

If you change ulim and mu to be COLUMN vectors, you will get a 2x1 return, since cdfMVne treats each row of ulim and mu as a separate set of inputs.

link

aptech

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