Re: Re: More weird integration issues...

*To*: mathgroup at smc.vnet.net*Subject*: [mg35765] Re: [mg35748] Re: [mg35728] More weird integration issues...*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Tue, 30 Jul 2002 07:22:15 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

It seems that you have not evaluated Binesh's defintion of F. You should be getting a numerical answer, not a formula involving F, Integrate etc. Andrzej On Monday, July 29, 2002, at 07:57 PM, DrBob wrote: > I get the same answer both ways, to as many places as you see here: > > 1.8430622009642987*Integrate[ > (-0.9025328739879791 + X)^5* > F[Subscript[p, 0], > 0.2856264419666387, > 0.04012528894153399, > 0.2662836604257217, > 0.7959934248376723, > 0.15354837805257518, X], > {X, -Infinity, Infinity}] > > I'm using Version 4.2. > > Bobby > > -----Original Message----- > From: Andrzej Kozlowski [mailto:andrzej at tuins.ac.jp] To: mathgroup at smc.vnet.net > Sent: Monday, July 29, 2002 2:13 AM > Subject: [mg35765] [mg35748] Re: [mg35728] More weird integration issues... > > 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 >> >> >> > > > > >