Will the function of these random variables be a sub-Gaussian distribution?
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Suppose a function $f(X,Y)$ is $sigma$-sub-gaussian when the random variables $X$and $Y$ are distributed independently of each other.
For example,
$f(mu,sigma) = exp(-frac{(x-mu)^2}{2sigma^2})$ where $sigma$ and $mu $ are distributed according to distribution $P_{mu}$ and $P_{sigma}$. Given they are independent $f(mu,sigma)$ will be distributed according to $P_{mu}.P_{sigma}$
My question is if now, $sigma$ and $mu $ are rather distributed jointly in a dependent fashion i.e. distributed according to $P_{mu,sigma}$ ,will the distribution still be sub-Gaussian ?
probability-distributions
asked Nov 17 at 21:57
vortex_sparrow
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up vote
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down vote
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Suppose a function $f(X,Y)$ is $sigma$-sub-gaussian when the random variables $X$and $Y$ are distributed independently of each other.
For example,
$f(mu,sigma) = exp(-frac{(x-mu)^2}{2sigma^2})$ where $sigma$ and $mu $ are distributed according to distribution $P_{mu}$ and $P_{sigma}$. Given they are independent $f(mu,sigma)$ will be distributed according to $P_{mu}.P_{sigma}$
My question is if now, $sigma$ and $mu $ are rather distributed jointly in a dependent fashion i.e. distributed according to $P_{mu,sigma}$ ,will the distribution still be sub-Gaussian ?
probability-distributions
asked Nov 17 at 21:57
vortex_sparrow
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose a function $f(X,Y)$ is $sigma$-sub-gaussian when the random variables $X$and $Y$ are distributed independently of each other.
For example,
$f(mu,sigma) = exp(-frac{(x-mu)^2}{2sigma^2})$ where $sigma$ and $mu $ are distributed according to distribution $P_{mu}$ and $P_{sigma}$. Given they are independent $f(mu,sigma)$ will be distributed according to $P_{mu}.P_{sigma}$
My question is if now, $sigma$ and $mu $ are rather distributed jointly in a dependent fashion i.e. distributed according to $P_{mu,sigma}$ ,will the distribution still be sub-Gaussian ?
probability-distributions
asked Nov 17 at 21:57
vortex_sparrow
11
Suppose a function $f(X,Y)$ is $sigma$-sub-gaussian when the random variables $X$and $Y$ are distributed independently of each other.
For example,
$f(mu,sigma) = exp(-frac{(x-mu)^2}{2sigma^2})$ where $sigma$ and $mu $ are distributed according to distribution $P_{mu}$ and $P_{sigma}$. Given they are independent $f(mu,sigma)$ will be distributed according to $P_{mu}.P_{sigma}$
My question is if now, $sigma$ and $mu $ are rather distributed jointly in a dependent fashion i.e. distributed according to $P_{mu,sigma}$ ,will the distribution still be sub-Gaussian ?
probability-distributions
probability-distributions
asked Nov 17 at 21:57
vortex_sparrow
11
asked Nov 17 at 21:57
vortex_sparrow
11
asked Nov 17 at 21:57
vortex_sparrow
11
asked Nov 17 at 21:57
vortex_sparrow
11
asked Nov 17 at 21:57
vortex_sparrow
11
11
add a comment |
add a comment |
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