Mixing
How to find moments/compute this integral?
$begingroup$
I have a steady state distribution which is of the form $$K[A+Bz]^{C}e^{D(1-z)}$$ where $A,ldots,D$ are constants. I want to find moments of $z$. I do not know how I might go about it so that I can get a closed form expression. My first instinct was to look at the Gamma function, but I have been unable to reduce this to a useful expression. The exact expressions for $A,ldots,D$ are as follows:
$A=4s$
$B=2c+h$
$C=frac{4Ns(c+h)}{(2c+h)^2}-1$
$D=frac{hN}{2(2c+h)}$
This seems to me a problem of manipulating constants right now, but I have been unable to get something I can work with with $A,B,D$. Any help is appreciated!
PS: $min[-1,1]$.
calculus probability integration moment-generating-functions
asked Jan 4 at 18:53
BoshuBoshu
705315
$endgroup$
add a comment |
$begingroup$
I have a steady state distribution which is of the form $$K[A+Bz]^{C}e^{D(1-z)}$$ where $A,ldots,D$ are constants. I want to find moments of $z$. I do not know how I might go about it so that I can get a closed form expression. My first instinct was to look at the Gamma function, but I have been unable to reduce this to a useful expression. The exact expressions for $A,ldots,D$ are as follows:
$A=4s$
$B=2c+h$
$C=frac{4Ns(c+h)}{(2c+h)^2}-1$
$D=frac{hN}{2(2c+h)}$
This seems to me a problem of manipulating constants right now, but I have been unable to get something I can work with with $A,B,D$. Any help is appreciated!
PS: $min[-1,1]$.
calculus probability integration moment-generating-functions
asked Jan 4 at 18:53
BoshuBoshu
705315
$endgroup$
add a comment |
$begingroup$
I have a steady state distribution which is of the form $$K[A+Bz]^{C}e^{D(1-z)}$$ where $A,ldots,D$ are constants. I want to find moments of $z$. I do not know how I might go about it so that I can get a closed form expression. My first instinct was to look at the Gamma function, but I have been unable to reduce this to a useful expression. The exact expressions for $A,ldots,D$ are as follows:
$A=4s$
$B=2c+h$
$C=frac{4Ns(c+h)}{(2c+h)^2}-1$
$D=frac{hN}{2(2c+h)}$
This seems to me a problem of manipulating constants right now, but I have been unable to get something I can work with with $A,B,D$. Any help is appreciated!
PS: $min[-1,1]$.
calculus probability integration moment-generating-functions
asked Jan 4 at 18:53
BoshuBoshu
705315
$endgroup$
I have a steady state distribution which is of the form $$K[A+Bz]^{C}e^{D(1-z)}$$ where $A,ldots,D$ are constants. I want to find moments of $z$. I do not know how I might go about it so that I can get a closed form expression. My first instinct was to look at the Gamma function, but I have been unable to reduce this to a useful expression. The exact expressions for $A,ldots,D$ are as follows:
$A=4s$
$B=2c+h$
$C=frac{4Ns(c+h)}{(2c+h)^2}-1$
$D=frac{hN}{2(2c+h)}$
This seems to me a problem of manipulating constants right now, but I have been unable to get something I can work with with $A,B,D$. Any help is appreciated!
PS: $min[-1,1]$.
calculus probability integration moment-generating-functions
calculus probability integration moment-generating-functions
asked Jan 4 at 18:53
BoshuBoshu
705315
asked Jan 4 at 18:53
BoshuBoshu
705315
asked Jan 4 at 18:53
BoshuBoshu
705315
asked Jan 4 at 18:53
BoshuBoshu
705315
asked Jan 4 at 18:53
BoshuBoshu
705315
705315
add a comment |
add a comment |
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