Re: More weird integration issues...

• To: mathgroup at smc.vnet.net
• Subject: [mg35748] Re: [mg35728] More weird integration issues...
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Mon, 29 Jul 2002 03:13:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```There does sem to be a bug here, but it is not quite what you think.
It's the first answer that you get that is probably wrong. On the other
hand, in the second case it is very unlikely that Mathematica enters an
infinite loop, rather it is still trying to arrive at the answer and
there is no guarantee that it will reach one after, say a week or a
month.

As for first case, the reason why the answer is probably this. Evaluate
the formula:

formula=Integrate[F[Subscript[p, 0], Subscript[p, 1], Subscript[p, 2],
Subscript[p, 3], Subscript[p, 4], Subscript[p, 5], X]*((X - m)/sd)^5,
{X, -Infinity, Infinity}]

Now set

Evaluate[Table[Subscript[p, i], {i, 1, 5}]] = Table[Random[], {5}]

and also

sd = Random[]; m = Random[];

Now evaluate again

Integrate[F[Subscript[p, 0], Subscript[p, 1], Subscript[p, 2],
Subscript[p, 3], Subscript[p, 4], Subscript[p, 5], X]*((X - m)/sd)^5,
{X, -Infinity, Infinity}]

and

formula

You will almost certainly get different answers, while they clearly
ought to be the same. It seems that it is nto the fact that the names
you are suing are different that leads to different results in both of
your integrals but the fact that the names of the parameters in the
first case are not symbols. "Officially" there is no reason why they
should be, but in practice using non-symbols in formulas makes them more
complicated and is more likely to result in errors.

The really bad news as far as your problem is concerned is that it is
the 6 hour fruitless computation that appears to be the correct one ...

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Saturday, July 27, 2002, at 07:43  PM, Binesh Bannerjee wrote:

> Hi. I'm trying to compute the 5th moment of a tweak to the normal pdf.
> Here's what I have:
>
> F[a_, b_, c_, d_, e_, f_, X_] := (a + b X + c X^2 + d X^3 + e X^4 + f
> X^5)*
>     Exp[-(((X - m)/sd)^2)/2]/(Sqrt[2Pi]sd)
>
> The strange thing, and I'd appreciate someone shedding some light on
> this,
> is that this:
>
> \!\(Integrate[
>     F[p\_0, p\_1, p\_2, p\_3, p\_4, p\_5,
>         X]*\((\((X - m)\)/sd)\)^5, {X, \(-Infinity\), Infinity},
>     Assumptions -> {sd > 0}]\)
>
> (I cut and pasted that it looks like it works)
>
> Anyway, THAT gives me an answer really quickly... (within 5 minutes on
> my box)
>
> JUST changing it from p0..5 to a,b,c,d,e,f like so:
>
> Integrate[F[a, b, c, d, e, f, X]*((X - m)/sd)^5, {X, -Infinity,
> Infinity},
>   Assumptions -> {sd > 0}]
>
> Causes mathematica to go into an infinite loop (seemingly after 6
> hours).
>
> This ... sucks. How am I to know if a certain equation is solvable, if
> only I choose the right variables??
>
> Binesh Bannerjee
>
> --
> "For in much wisdom is much grief, and he that increaseth knowledge
>  increaseth sorrow." -- Ecclesiastes 1:18
>
>     PGP  Key: http://www.hex21.com/~binesh/binesh-public.asc
>     SSH2 Key: http://www.hex21.com/~binesh/binesh-ssh2.pub
>     SSH1 Key: http://www.hex21.com/~binesh/binesh-ssh1.pub
> OpenSSH  Key: http://www.hex21.com/~binesh/binesh-openssh.pub
>
>
>

```

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