A8
发帖数: 20 | 1 先谢过了.. 有包子奖励..
Two dependent continuous random variable X=h(W), Y=g(W), W is un underlying random
variable. Both X and Y have strictly positive density on R or the same valid domain. fx(x)>0, and fy(y)>0. I want to know if Z=X+Y have strictly positive density or not, fz(z)>0
on the domain???
I forgot to say that g and h are known functions. for example, both X and Y could be lognormals with different parameters, but with the same underlying normal random variable W.
While the density of Z=X+Y, fz(z)>0 strictly on the domain are my favoriate result..
Thanks...
牛人们能给点证明的建议不..
多谢多谢 | i***k
发帖数: 4 | 2 X=W
Y=-W
underlying random
fy(
>0
【在 A8 的大作中提到】
: 先谢过了.. 有包子奖励..
: Two dependent continuous random variable X=h(W), Y=g(W), W is un underlying random
: variable. Both X and Y have strictly positive density on R or the same valid domain. fx(x)>0, and fy(y)>0. I want to know if Z=X+Y have strictly positive density or not, fz(z)>0
: on the domain???
: I forgot to say that g and h are known functions. for example, both X and Y could be lognormals with different parameters, but with the same underlying normal random variable W.
: While the density of Z=X+Y, fz(z)>0 strictly on the domain are my favoriate result..
: Thanks...
: 牛人们能给点证明的建议不..
: 多谢多谢
| A8
发帖数: 20 | 3 Thanks. I forgot to say that g and h are known functions. Both X and Y could be lognormals with different parameters, but with the same underlying normal random variable W.
While the density of Z=X+Y, fz(z)>0 strictly are my favoriate result..
Thanks...
【在 i***k 的大作中提到】
: X=W
: Y=-W
:
: underlying random
: fy(
: >0
| i***k
发帖数: 4 | 4 lognormal does not have strictly positive density on R.
could be lognormals with different parameters, but with the same underlying
normal random variable W.
【在 A8 的大作中提到】
: Thanks. I forgot to say that g and h are known functions. Both X and Y could be lognormals with different parameters, but with the same underlying normal random variable W.
: While the density of Z=X+Y, fz(z)>0 strictly are my favoriate result..
: Thanks...
| A8
发帖数: 20 | 5 I mean for example X Y could be log normal, but in this case the domain
should be R+, both X and Y have the same domain
Thanks..
underlying
【在 i***k 的大作中提到】
: lognormal does not have strictly positive density on R.
:
: could be lognormals with different parameters, but with the same underlying
: normal random variable W.
| l*********s
发帖数: 5409 | 6 counter example. w support is 0 - +inf, x and y are exp(w) from 1 to inf.
z=x+y is from 2 to inf. the support is different than x and y's.
【在 A8 的大作中提到】
: I mean for example X Y could be log normal, but in this case the domain
: should be R+, both X and Y have the same domain
: Thanks..
:
: underlying
| A8
发帖数: 20 | 7 Thanks for your input.
Good point. As long as the density is greater than zero on the valid support, it should be fine for me. In my case w is normal, so x, y z have the same support
.
Thanks...
【在 l*********s 的大作中提到】
: counter example. w support is 0 - +inf, x and y are exp(w) from 1 to inf.
: z=x+y is from 2 to inf. the support is different than x and y's.
| l*********s
发帖数: 5409 | 8 since f(x) is nonnegative, so as long as the support of Z is the same as X
and Y, you are set.
support, it should be fine for me. In my case w is normal, so x, y z have
the same support
【在 A8 的大作中提到】
: Thanks for your input.
: Good point. As long as the density is greater than zero on the valid support, it should be fine for me. In my case w is normal, so x, y z have the same support
: .
: Thanks...
| A8
发帖数: 20 | 9 I am thinking since X and Y are dependent. If we have Z=X+Y, is there possiblity that at some point, that f(z)=0.Like at this point the dF/dz=0, Although F(z) do not have flat piece.
Which makes f(z) not strictly greater than 0 at particular point on the
support.
Thanks, guys... I'll FA BAOZI to you guys tonight...
【在 l*********s 的大作中提到】
: since f(x) is nonnegative, so as long as the support of Z is the same as X
: and Y, you are set.
:
: support, it should be fine for me. In my case w is normal, so x, y z have
: the same support
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