x********o
发帖数: 519 | 1 suppose X and Y are two R. V with uniform distribution on [0,1], the
correlation between X and Y is rho,
what's the density function of X+Y? | z****g
发帖数: 1978 | | c**********e
发帖数: 2007 | 3 Can construct it in the following way:
X, Z ~ uniform on [0,1]. W ~ Bin(1, rho).
All three are independent. Let Y=WX + (1-W)Z
Then X and Y have corr rho.
The density of X+Y is
rho/2 + (1-rho)t for t<=1
rho/2 + (1-rho)(1-t) for 1<=t<=2.
【在 x********o 的大作中提到】
: suppose X and Y are two R. V with uniform distribution on [0,1], the
: correlation between X and Y is rho,
: what's the density function of X+Y?
| n******t
发帖数: 4406 | 4 not determined.
【在 x********o 的大作中提到】
: suppose X and Y are two R. V with uniform distribution on [0,1], the
: correlation between X and Y is rho,
: what's the density function of X+Y?
| x********o
发帖数: 519 | 5 nice solution.
ps: there might be a small typo in your answer
【在 c**********e 的大作中提到】
: Can construct it in the following way:
: X, Z ~ uniform on [0,1]. W ~ Bin(1, rho).
: All three are independent. Let Y=WX + (1-W)Z
: Then X and Y have corr rho.
: The density of X+Y is
: rho/2 + (1-rho)t for t<=1
: rho/2 + (1-rho)(1-t) for 1<=t<=2.
| w**********y
发帖数: 1691 | 6 这个不是典型的convulsion么?画个图..对f1(x)f2(z-x)dx 求积分得到z的density
function | k*******d
发帖数: 1340 | 7 Not convolution. x and y are not independent.
Of course, in general, as long as one can write the joint pdf of x and y,
the pdf of X+Y will be \int f(x,z-x)dx, with convolution being a special
case.
【在 w**********y 的大作中提到】
: 这个不是典型的convulsion么?画个图..对f1(x)f2(z-x)dx 求积分得到z的density
: function
| w**********y
发帖数: 1691 | 8 哦,没仔细看题..thx
【在 k*******d 的大作中提到】
: Not convolution. x and y are not independent.
: Of course, in general, as long as one can write the joint pdf of x and y,
: the pdf of X+Y will be \int f(x,z-x)dx, with convolution being a special
: case.
| r***n
发帖数: 6 | 9 精辟
【在 z****g 的大作中提到】
: Gaussian copula.
| a****c
发帖数: 978 | | p******y
发帖数: 5 | 11 Not really, the question asks for density for X+Y, not the joint density of
X and Y.
【在 r***n 的大作中提到】
: 精辟
| c*********g
发帖数: 37 | 12 then the answer depends on Z.
right ?
【在 c**********e 的大作中提到】
: Can construct it in the following way:
: X, Z ~ uniform on [0,1]. W ~ Bin(1, rho).
: All three are independent. Let Y=WX + (1-W)Z
: Then X and Y have corr rho.
: The density of X+Y is
: rho/2 + (1-rho)t for t<=1
: rho/2 + (1-rho)(1-t) for 1<=t<=2.
|
|
