# Finding support for multivariate transformation

• MHB
• lemonthree
This can also be represented as $0 < z < w^2 < 1$.In summary, the joint transformation of (X,Y) can be described by the support of (Z,W) which is a quadrant-like shape with the boundaries $0 < \sqrt{z} < w < 1$ and $0 < z < 1$. This can also be represented as $0 < z < w^2 < 1$.
lemonthree
For the given joint pdf of X and Y $$f(x,y) = 12xy(1 - y); 0 < x < 1; 0 < y < 1$$
Let $Z = XY^2$ and $W = Y$ be a joint transformation of (X,Y)

Sketch the graph of the support of $(Z,W)$ and describe it
mathematically.

I'm not very sure how to describe (Z,W).
First, I draw the graph of the support of X and Y, which is a rectangular support.

Now I "map" each interval over to (Z,W).

For $x=0, 0<y<1, z=0, 0<w<1$

For $x=1, 0<y<1, 0<z<w^2, 0<w<1$

For $y=0, 0<x<1, z=0, w=0$

For $y=1, 0<x<1, 0<z<1, w=1$

I'm not quite sure how to describe (Z,W), this isn't rectangular neither is it triangular. I have drawn the graph of what I think is the support of (Z,W). How do I describe this quadrant-like support? $0<w<1, 0<z<1, \sqrt{z}<w<1$?

After some figuring out, I determined that the description of the support is all as described in the graph drawn. $0 < \sqrt{z} < w < 1$

## 1. What is multivariate transformation?

Multivariate transformation is a statistical technique used to transform a set of variables into a new set of variables that are more easily interpretable or have a specific desired property. It involves combining and manipulating multiple variables to create a new set of variables that better represent the data.

## 2. Why is finding support for multivariate transformation important?

Finding support for multivariate transformation is important because it allows researchers to better understand complex relationships among variables and to identify underlying patterns in the data. It can also help improve the accuracy and efficiency of statistical models and analyses.

## 3. How do you determine the appropriate multivariate transformation for your data?

The appropriate multivariate transformation for your data depends on the specific goals of your research and the characteristics of your data. Some common techniques for determining the appropriate transformation include visual inspection of data, statistical tests, and consulting with experts in the field.

## 4. What are some common types of multivariate transformations?

Some common types of multivariate transformations include principal component analysis, factor analysis, discriminant analysis, and canonical correlation analysis. Each of these techniques has different goals and assumptions, so it is important to carefully consider which one is most appropriate for your data.

## 5. How do you assess the effectiveness of a multivariate transformation?

The effectiveness of a multivariate transformation can be assessed through various methods, such as examining the distribution of transformed variables, evaluating the correlation between the original and transformed variables, and assessing the performance of statistical models using the transformed variables. It is also important to consider the interpretability and usefulness of the transformed variables in relation to the research goals.

• Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
631
• Set Theory, Logic, Probability, Statistics
Replies
6
Views
4K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
10
Views
1K
• Differential Equations
Replies
5
Views
986
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
948
• Calculus
Replies
6
Views
647
• Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K