Simplify $int F(x+a)dF(x)$
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Any hints on how to simplify
$$int_a^b F(x+c)dF(x),$$
where $a,b,c in mathbbR^+$, $F(x)$ is a CDF of random variable $X$ and its PDF $f(x)$ is continuously differentiable over the support $[-infty, infty].$
I played around with integration by parts, but did not achieve too much.
integration definite-integrals
add a comment |Â
up vote
3
down vote
favorite
Any hints on how to simplify
$$int_a^b F(x+c)dF(x),$$
where $a,b,c in mathbbR^+$, $F(x)$ is a CDF of random variable $X$ and its PDF $f(x)$ is continuously differentiable over the support $[-infty, infty].$
I played around with integration by parts, but did not achieve too much.
integration definite-integrals
1
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Any hints on how to simplify
$$int_a^b F(x+c)dF(x),$$
where $a,b,c in mathbbR^+$, $F(x)$ is a CDF of random variable $X$ and its PDF $f(x)$ is continuously differentiable over the support $[-infty, infty].$
I played around with integration by parts, but did not achieve too much.
integration definite-integrals
Any hints on how to simplify
$$int_a^b F(x+c)dF(x),$$
where $a,b,c in mathbbR^+$, $F(x)$ is a CDF of random variable $X$ and its PDF $f(x)$ is continuously differentiable over the support $[-infty, infty].$
I played around with integration by parts, but did not achieve too much.
integration definite-integrals
asked Aug 22 at 6:43
Green.H
1,057216
1,057216
1
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22
add a comment |Â
1
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22
1
1
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22
add a comment |Â
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1
This is the so-called convolution of $F$ with itself evaluated at $-c$. There is no general formula for this.
â Kavi Rama Murthy
Aug 22 at 7:22