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#1 2012-04-30 19:35:06

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Normal Probability Integration

up

Last edited by George,Y (2012-04-30 19:36:56)


X'(y-Xβ)=0

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#2 2013-11-28 04:35:06

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Hi;

I do not think there are closed forms for either of those. But if you could put some bounds on some of the constants an asymptotic form might be possible.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-12-14 15:59:14

George,Y
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Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration

There actually is closed form, but through a different integration.


X'(y-Xβ)=0

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#4 2013-12-14 19:14:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

A different integration?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-12-15 15:25:05

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration

bobbym wrote:

A different integration?

I have found a way to integrate this directly, but it is very tricky.


X'(y-Xβ)=0

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#6 2013-12-15 18:24:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

I doubt that.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-12-15 22:41:00

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

I would say it is unlikely to but the whole question could be answered by posting the solution. Then it can be checked.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2013-12-16 08:43:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

http://m.wolframalpha.com/input/?i=inte … E2&x=0&y=0

Last edited by anonimnystefy (2013-12-17 01:29:39)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2013-12-16 12:39:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Hi;

That is not his integral.

But even if it were, that is not in closed form.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#10 2013-12-16 17:46:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

It is not his integral, but his can be manipulated into that one with substitutions and manipulations. The point is that Alpha says there's no closed form...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2013-12-17 00:45:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Hi;

Have you looked at the integral you sent to Alpha in post #8?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2013-12-17 01:20:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

Yes, I have.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2013-12-17 01:20:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Then you know it is not and can never be his integral.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#14 2013-12-17 01:29:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

Fixed.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2013-12-17 01:40:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Brings us back to post #7. The fact that both M's can not do the integral does mean there is a high probability that it is intractable. But they are not infallible, so I think if George would post his answer the whole thing can resolved quickly.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#16 2013-12-17 01:59:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

Do you think some progress can be made using DUIT?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2013-12-17 02:11:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

I have not tried but it sure does respond well to numerical integration for any T.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2013-12-29 01:11:53

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration

Sorry guys, I made a mistake, the question should be:

Last edited by George,Y (2013-12-29 01:12:55)


X'(y-Xβ)=0

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#19 2013-12-29 02:22:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Normal Probability Integration

That does not change much.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#20 2013-12-29 03:29:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Hi George,Y;

That does not change much.

Yes, I think it is time to show your solution. I am willing to bet 21% of my bankroll, a whopping $1.16 that the solution is wrong.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#21 2013-12-30 22:09:00

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration



Last edited by George,Y (2013-12-30 22:11:21)


X'(y-Xβ)=0

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#22 2013-12-30 22:16:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

Hi;

What is d?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#23 2013-12-30 22:16:59

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration

After this change of variable, I think now the question is easier.


X'(y-Xβ)=0

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#24 2013-12-30 22:21:05

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Normal Probability Integration

bobbym wrote:

Hi;

What is d?

d is the differential operator


X'(y-Xβ)=0

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#25 2013-12-30 22:22:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Normal Probability Integration

What is the new integral?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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