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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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  • $\begingroup$ What do you a weighted probability density? Is it the density for the weighted random variable? Please write out your variables in a mathematical form. $\endgroup$ – Gordon Jun 24 '16 at 18:38

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