Product of two Beta distributed random variables
I have two Beta distributed random variables :
$X_1=B(alpha_1, beta_1)$
$X_2=B(alpha_2, beta_2)$
What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?
probability-distributions beta-function
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
add a comment |
I have two Beta distributed random variables :
$X_1=B(alpha_1, beta_1)$
$X_2=B(alpha_2, beta_2)$
What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?
probability-distributions beta-function
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
1
See this.
– Clement C.
Dec 18 '14 at 14:53
1
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31
add a comment |
I have two Beta distributed random variables :
$X_1=B(alpha_1, beta_1)$
$X_2=B(alpha_2, beta_2)$
What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?
probability-distributions beta-function
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
I have two Beta distributed random variables :
$X_1=B(alpha_1, beta_1)$
$X_2=B(alpha_2, beta_2)$
What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?
probability-distributions beta-function
probability-distributions beta-function
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
asked Dec 18 '14 at 14:48
GuillaumeThomas
16816
16816
1
See this.
– Clement C.
Dec 18 '14 at 14:53
1
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31
add a comment |
1
See this.
– Clement C.
Dec 18 '14 at 14:53
1
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31
1
1
See this.
– Clement C.
Dec 18 '14 at 14:53
See this.
– Clement C.
Dec 18 '14 at 14:53
1
1
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31
add a comment |
2 Answers
2
active
oldest
votes
There are several paper for this problem. See for example:
- On the Distribution of the Product of Independent Beta Random Variables
– Applications - Products of Beta distributed random variables
- BETA PRODUCTS WITH COMPLEX PARAMETERS
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
add a comment |
You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem
answered Dec 18 '14 at 14:56
Jean-Robert
1563
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
There are several paper for this problem. See for example:
- On the Distribution of the Product of Independent Beta Random Variables
– Applications - Products of Beta distributed random variables
- BETA PRODUCTS WITH COMPLEX PARAMETERS
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
add a comment |
There are several paper for this problem. See for example:
- On the Distribution of the Product of Independent Beta Random Variables
– Applications - Products of Beta distributed random variables
- BETA PRODUCTS WITH COMPLEX PARAMETERS
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
add a comment |
There are several paper for this problem. See for example:
- On the Distribution of the Product of Independent Beta Random Variables
– Applications - Products of Beta distributed random variables
- BETA PRODUCTS WITH COMPLEX PARAMETERS
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
There are several paper for this problem. See for example:
- On the Distribution of the Product of Independent Beta Random Variables
– Applications - Products of Beta distributed random variables
- BETA PRODUCTS WITH COMPLEX PARAMETERS
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
answered Dec 18 '14 at 15:21
alexjo
12.2k1329
12.2k1329
add a comment |
add a comment |
You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem
answered Dec 18 '14 at 14:56
Jean-Robert
1563
add a comment |
You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem
answered Dec 18 '14 at 14:56
Jean-Robert
1563
add a comment |
You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem
answered Dec 18 '14 at 14:56
Jean-Robert
1563
You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem
answered Dec 18 '14 at 14:56
Jean-Robert
1563
answered Dec 18 '14 at 14:56
Jean-Robert
1563
answered Dec 18 '14 at 14:56
Jean-Robert
1563
answered Dec 18 '14 at 14:56
Jean-Robert
1563
1563
add a comment |
add a comment |
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1
See this.
– Clement C.
Dec 18 '14 at 14:53
1
A general solution is derived at math.stackexchange.com/questions/1201321/…
– wolfies
Sep 23 '17 at 8:15
Do not forget to state that $X_1$ and $X_2$ are independent!
– Jeppe Stig Nielsen
Dec 6 '18 at 12:31