Mixing
Sum of Beta Random Variables
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Supose I have $I$ independently (but not necessarily identically) distributed beta random variables, $X_i = text{beta}(alpha_i,beta_i)$, for $i=1,dots,I$.
Is there a known distribution for the sum of these r.v.s, $Y=sum_i X_i$?
Furthermore, is there a known distribution for the mixture of these r.v.s, as in $Y=sum_i omega_i X_i$, where $sum_i omega_i = 1$?
statistics probability-distributions random-variables
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
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add a comment |
$begingroup$
Supose I have $I$ independently (but not necessarily identically) distributed beta random variables, $X_i = text{beta}(alpha_i,beta_i)$, for $i=1,dots,I$.
Is there a known distribution for the sum of these r.v.s, $Y=sum_i X_i$?
Furthermore, is there a known distribution for the mixture of these r.v.s, as in $Y=sum_i omega_i X_i$, where $sum_i omega_i = 1$?
statistics probability-distributions random-variables
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
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$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
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– Gabriel Romon
Feb 1 at 16:08
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Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26
add a comment |
$begingroup$
Supose I have $I$ independently (but not necessarily identically) distributed beta random variables, $X_i = text{beta}(alpha_i,beta_i)$, for $i=1,dots,I$.
Is there a known distribution for the sum of these r.v.s, $Y=sum_i X_i$?
Furthermore, is there a known distribution for the mixture of these r.v.s, as in $Y=sum_i omega_i X_i$, where $sum_i omega_i = 1$?
statistics probability-distributions random-variables
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
$endgroup$
Supose I have $I$ independently (but not necessarily identically) distributed beta random variables, $X_i = text{beta}(alpha_i,beta_i)$, for $i=1,dots,I$.
Is there a known distribution for the sum of these r.v.s, $Y=sum_i X_i$?
Furthermore, is there a known distribution for the mixture of these r.v.s, as in $Y=sum_i omega_i X_i$, where $sum_i omega_i = 1$?
statistics probability-distributions random-variables
statistics probability-distributions random-variables
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
asked Feb 1 at 15:52
Ethan ArensonEthan Arenson
1
1
$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
$endgroup$
– Gabriel Romon
Feb 1 at 16:08
$begingroup$
Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26
add a comment |
$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
$endgroup$
– Gabriel Romon
Feb 1 at 16:08
$begingroup$
Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26
$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
$endgroup$
– Gabriel Romon
Feb 1 at 16:08
$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
$endgroup$
– Gabriel Romon
Feb 1 at 16:08
$begingroup$
Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26
$begingroup$
Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26
add a comment |
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$begingroup$
Relevant: math.stackexchange.com/questions/85535/…
$endgroup$
– Gabriel Romon
Feb 1 at 16:08
$begingroup$
Not in closed form. There isn't even a closed form expression for the PDF of the sum in the case $n=2$.
$endgroup$
– Robert Israel
Feb 1 at 16:26