What do you think it should be?Hi all,
maybe it is a dumb question but hopefully somebody can help me.
What is the integral of: [math]\int_{a}^{b} F(x)^{(n-1)}\,dx[/math]
Tank you very much.
Chris
I do not think a general solution is available - with the information given in the post.Is it possible to have a general solution without knowing F(x) in the first place. This is part of a general proof. The idea is to solve it for "every" distribution F(x).
Does [imath]F(x)^{(n-1)}[/imath] by chance stand for the [imath](n-1)[/imath]-th derivative of [imath]F(x)[/imath] ?Hi all,
maybe it is a dumb question but hopefully somebody can help me.
What is the integral of: [math]\int_{a}^{b} F(x)^{(n-1)}\,dx[/math]
Tank you very much.
Chris
There may be more to say if you show that larger problem, to give context. There may be a different way to attack that problem, or it may provide additional information you have omitted.Is it possible to have a general solution without knowing F(x) in the first place. This is part of a general proof. The idea is to solve it for "every" distribution F(x).
F(x) must follow a particular probability distribution...The calculation is out of a proof for the optimal bidding strategy in an auction. It's part of game theory in economics.
The optimal bid b(x) in an auction, given an value x that is distributed on an Interval [0,1] according to a function F(x) is:
[math]b(x) = x -\int_{a}^{b} F(x)^{(n-1)} \,dx \cdot \dfrac{1}{F(x)^{n-1}}+........[/math]
I can perform all the proofs for general distributions but I am stuck here. This is not a question in a class. It's a proof that i try to do by myself.
Can you provide a reference for the expression quoted above?The calculation is out of a proof for the optimal bidding strategy in an auction. It's part of game theory in economics.
The optimal bid b(x) in an auction, given an value x that is distributed on an Interval [0,1] according to a function F(x) is:
[math]b(x) = x -\int_{a}^{b} F(x)^{(n-1)} \,dx \cdot \dfrac{1}{F(x)^{n-1}}+........[/math]
I can perform all the proofs for general distributions but I am stuck here. This is not a question in a class. It's a proof that i try to do by myself.
Sorry, i should have stated what n stands for. n is the number of players. So, it is not the (n-1) derivative of F(v).Does [imath]F(x)^{(n-1)}[/imath] by chance stand for the [imath](n-1)[/imath]-th derivative of [imath]F(x)[/imath] ?
You can find a similar calculation in a published paper. http://vita.mcafee.cc/PDF/JEL.pdf see page 12 (or 709).Can you provide a reference for the expression quoted above?
Can you please answer the question posed in response #6?
So what does that notation mean? [imath](n-1)[/imath]-th power of [imath]F[/imath], or just a superscript used for indexing? Also, what is [imath]F[/imath]? Is there a formula for it?Sorry, i should have stated what n stands for. n is the number of players. So, it is not the (n-1) derivative of F(v).