My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 25th, 2010, 12:22 PM   #1
Newbie
 
Joined: Jan 2010

Posts: 1
Thanks: 0

is this gaussian?

Is the following density gaussian?:
Code:
f(x,y)=A*exp[-1/2*(x^2+y^2-2*p*x*y)]
where A is the appropriate normalizing constant and p is the correlation between x and y. The marginal densities for x and y are indeed normal. I have a book that claims it 2d gaussian, but I can't figure out what the covariance matrix would be... it isn't [[1 p] [p 1]] because f doesn't have the 1/(1-p^2) in the denominator of the exponential... help?

More general question: are all exponentials of quadratic functions gaussian? This seems to be true for the univariate case but can't confirm for multivariate.
tomgrayson is offline  
 
January 25th, 2010, 01:19 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,762
Thanks: 697

Re: is this gaussian?

Let y=px+u. Then As a function of x and u you will have two independent Guassian terms. I'll confess to being a little rusty here, so I'll let you work out the details.

As for your second question, the answer is yes except for singularities (such as p=1).
mathman is online now  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
gaussian



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Gaussian coefficients sigma123 Advanced Statistics 1 January 18th, 2013 07:05 PM
Gaussian Integral mathbalarka Calculus 7 September 4th, 2012 10:15 AM
Gaussian elimination ewuc Algebra 2 September 17th, 2011 12:59 PM
The Gaussian integers Hagi Abstract Algebra 2 February 27th, 2011 12:03 AM
GCD, Gaussian integers Z[i] The Chaz Abstract Algebra 6 February 3rd, 2011 10:24 PM





Copyright © 2019 My Math Forum. All rights reserved.