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coupling of distributions vs joint distributions

0

$begingroup$

For continuoues variables, how is a coupling of two distributions different from their joint distribution? Are they the same concepts?

Update: Coupling is the same as defining a joint distribution on the Cartesian product space of the supports of original random variables, in a way that marginals of the defined joint distribution are equal to the original random variables. What am I missing?

probability probability-distributions coupling

share|cite|improve this question

edited Mar 26 at 14:00

user25004

asked Mar 25 at 21:04

user25004user25004

1,45011637

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Coupling of distributions has no relation to joint distributions. Coupling refers to taking random variables defined on different prob. spaces on putting equivalent variables (same distribution) on a single prob. space. en.wikipedia.org/wiki/Coupling_(probability)
  $endgroup$
  – herb steinberg
  Mar 25 at 21:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Even your explanation still seems like defining a joint distribution on the product space of the supports of original random variables, in a way that marginals of the defined joint distribution are equal to the original random variables. What am I missing?
  $endgroup$
  – user25004
  Mar 25 at 23:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My understanding is that coupling means defining random variables on the same probability space with the same distribution as those on separate spaces. This is my reading of the wikipedia reference. I personally am not familiar with the term "coupling distributions"..
  $endgroup$
  – herb steinberg
  Mar 26 at 2:50
  

  
  
  
  

add a comment | 

0

$begingroup$

For continuoues variables, how is a coupling of two distributions different from their joint distribution? Are they the same concepts?

Update: Coupling is the same as defining a joint distribution on the Cartesian product space of the supports of original random variables, in a way that marginals of the defined joint distribution are equal to the original random variables. What am I missing?

probability probability-distributions coupling

share|cite|improve this question

edited Mar 26 at 14:00

user25004

asked Mar 25 at 21:04

user25004user25004

1,45011637

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Coupling of distributions has no relation to joint distributions. Coupling refers to taking random variables defined on different prob. spaces on putting equivalent variables (same distribution) on a single prob. space. en.wikipedia.org/wiki/Coupling_(probability)
  $endgroup$
  – herb steinberg
  Mar 25 at 21:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Even your explanation still seems like defining a joint distribution on the product space of the supports of original random variables, in a way that marginals of the defined joint distribution are equal to the original random variables. What am I missing?
  $endgroup$
  – user25004
  Mar 25 at 23:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My understanding is that coupling means defining random variables on the same probability space with the same distribution as those on separate spaces. This is my reading of the wikipedia reference. I personally am not familiar with the term "coupling distributions"..
  $endgroup$
  – herb steinberg
  Mar 26 at 2:50
  

  
  
  
  

add a comment | 

$begingroup$

For continuoues variables, how is a coupling of two distributions different from their joint distribution? Are they the same concepts?

Update: Coupling is the same as defining a joint distribution on the Cartesian product space of the supports of original random variables, in a way that marginals of the defined joint distribution are equal to the original random variables. What am I missing?

probability probability-distributions coupling

share|cite|improve this question

edited Mar 26 at 14:00

user25004

asked Mar 25 at 21:04

user25004user25004

1,45011637

$endgroup$

share|cite|improve this question

edited Mar 26 at 14:00

user25004

asked Mar 25 at 21:04

user25004user25004

1,45011637

share|cite|improve this question

edited Mar 26 at 14:00

user25004

asked Mar 25 at 21:04

user25004user25004

1,45011637

asked Mar 25 at 21:04

user25004user25004

1,45011637

asked Mar 25 at 21:04

user25004user25004

1,45011637