Transformation integral
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I am studying a proof and have some difficulty understanding the following step:
$intlimits_0^infty y dF(t+y) = intlimits_0^infty (1-F(t+y))dy$.
Here, F(x) is probability distribution function.
Could somebody explain this equality?
Thank you very much in advance!
probability integration
asked Nov 23 at 15:44
Luna
84
add a comment |
up vote
0
down vote
favorite
I am studying a proof and have some difficulty understanding the following step:
$intlimits_0^infty y dF(t+y) = intlimits_0^infty (1-F(t+y))dy$.
Here, F(x) is probability distribution function.
Could somebody explain this equality?
Thank you very much in advance!
probability integration
asked Nov 23 at 15:44
Luna
84
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am studying a proof and have some difficulty understanding the following step:
$intlimits_0^infty y dF(t+y) = intlimits_0^infty (1-F(t+y))dy$.
Here, F(x) is probability distribution function.
Could somebody explain this equality?
Thank you very much in advance!
probability integration
asked Nov 23 at 15:44
Luna
84
I am studying a proof and have some difficulty understanding the following step:
$intlimits_0^infty y dF(t+y) = intlimits_0^infty (1-F(t+y))dy$.
Here, F(x) is probability distribution function.
Could somebody explain this equality?
Thank you very much in advance!
probability integration
probability integration
asked Nov 23 at 15:44
Luna
84
asked Nov 23 at 15:44
Luna
84
asked Nov 23 at 15:44
Luna
84
asked Nov 23 at 15:44
Luna
84
asked Nov 23 at 15:44
Luna
84
84
add a comment |
add a comment |
1 Answer
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Hint: Put $g(y)=1-F(t+y)$, and $h(y)=y$ in
$$int_{a}^{b} g(y) h'(y) dy = g(y)h(y)|_a^{b} -int_{a}^{b} h(y) g'(y) dy.$$
answered Nov 23 at 15:50
Math Lover
13.6k31435
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Hint: Put $g(y)=1-F(t+y)$, and $h(y)=y$ in
$$int_{a}^{b} g(y) h'(y) dy = g(y)h(y)|_a^{b} -int_{a}^{b} h(y) g'(y) dy.$$
answered Nov 23 at 15:50
Math Lover
13.6k31435
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
add a comment |
up vote
0
down vote
Hint: Put $g(y)=1-F(t+y)$, and $h(y)=y$ in
$$int_{a}^{b} g(y) h'(y) dy = g(y)h(y)|_a^{b} -int_{a}^{b} h(y) g'(y) dy.$$
answered Nov 23 at 15:50
Math Lover
13.6k31435
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
add a comment |
up vote
0
down vote
up vote
0
down vote
Hint: Put $g(y)=1-F(t+y)$, and $h(y)=y$ in
$$int_{a}^{b} g(y) h'(y) dy = g(y)h(y)|_a^{b} -int_{a}^{b} h(y) g'(y) dy.$$
answered Nov 23 at 15:50
Math Lover
13.6k31435
Hint: Put $g(y)=1-F(t+y)$, and $h(y)=y$ in
$$int_{a}^{b} g(y) h'(y) dy = g(y)h(y)|_a^{b} -int_{a}^{b} h(y) g'(y) dy.$$
answered Nov 23 at 15:50
Math Lover
13.6k31435
answered Nov 23 at 15:50
Math Lover
13.6k31435
answered Nov 23 at 15:50
Math Lover
13.6k31435
answered Nov 23 at 15:50
Math Lover
13.6k31435
13.6k31435
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
add a comment |
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
Thanks for your response!
– Luna
Nov 23 at 16:10
Thanks for your response!
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
But how should I compute $(1-F(t+y)y mid^infty_0$ ?
– Luna
Nov 23 at 16:10
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
Some CDFs have the property that $lim_{ytoinfty}y(1-F(t+y))=0$.
– Math Lover
Nov 23 at 16:44
add a comment |
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