Weighting Variables in Multivariate Normal Density Calculations

Summary

The document asks how to give one variable more influence when calculating multivariate normal probability densities for observations relative to a specified mean. It describes a four-variable example using an identity covariance matrix, reports density values for five observations, and normalizes those values so they sum to one. The author’s goal is to make the fourth variable count three times as much in the distance-like comparison.

No answer or weighting method is included, so the example does not establish how to modify the covariance matrix or whether the proposed density interpretation is appropriate. The reported values only show the result of the unweighted calculation under the stated identity covariance assumption. This is a focused statistical question with a concrete setup, rather than a complete procedure or an evaluated trading strategy.

Key ideas

• The example uses a multivariate normal density to compare observations with a reference mean.
• An identity covariance matrix gives the variables equal variance and no covariance in the stated calculation.
• The author asks how to increase the influence of one variable in the density calculation.
• The document reports normalized densities but provides no weighting solution or validation.

Tags

# weighted probability densities in matlab


# weighted probability densities in matlab












```
I have a set of variables (lets say a nx3 : 3 variables and n rows). I 
set the mean to be my current data (1x3); data for 3 variables as of 
today and set my covariance matrix as the identity matrix. I then
calculate the  probability density using the mnvpd function in matlab. In                
essence these probability densities are my "distances" from my current 
data (my mean variable)

My question is if I want to compute a weighted probability density how do
I do that? if i want to weight one variable 3x the others.

Based on my most recent value(my Mean parameter) the last data point has
the highest weight(closest distance). My question is how do I assign the
4th variable to have for example 3x more weight so that its reflected in
my calculation of densities.

X is my variable matrix, MU = [0.6638 -0.43 -1.56 0.45]
```

X =

```
0.7926   -1.1549   -0.9966    0.0520
0.7399   -0.8464   -1.4008    0.1385
0.7428   -0.5986   -1.3788    0.1682
0.3965   -0.4491   -1.2558    0.2441
0.6638   -0.4265   -1.5430    0.4194
```

Y = mvnpdf(X, MU, eye(4))

Y =

```
0.0152
0.0218
0.0235
0.0228
0.0253
```

Y/sum(Y) =

```
0.1401
0.2004
0.2165
0.2101
0.2329
```

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