RE: A Bug?
- To: mathgroup at smc.vnet.net
- Subject: [mg35322] RE: [mg35277] A Bug?
- From: "DrBob" <majort at cox-internet.com>
- Date: Mon, 8 Jul 2002 03:17:26 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
There's a bug, but not the one you think. "Indeterminate" is the right answer to your problem, because for F[x]==1 and i==n, we have the term Binomial[n, n] 1^n (1 - 1)^(n - n) This involves 0^0, which is Indeterminate. Contrast this with what happens when you use SetDelayed rather than Set: Clear[F, oStatCDF] oStatCDF[x_, r_, n_, F_] := Sum[Binomial[n, i] F[x]^i (1 - F[x])^(n - i), {i, r, n}] F[x_] := 1 oStatCDF[x, r, n, F] 0 THAT is a bug. Bobby -----Original Message----- From: Johannes Ludsteck To: mathgroup at smc.vnet.net [mailto:johannes.ludsteck at wiwi.uni-regensburg.de] Subject: [mg35322] [mg35277] A Bug? Dear MathGroup members, let Mathematica evaluate In[1]:= oStatCDF[x_,r_,n_,F_]= Sum[Binomial[n,i] F[x]^i (1-F[x])^(n-i), {i,r,n}] Out[1]= (1 - F[x])^(n - r) F[x]^r Gamma[1 + n] Hypergeometric2F1[1,-n + r, 1 + r, -F[x]/(1 - F[x])]/ (Gamma[1 + n - r] Gamma[1 + r]) Looks fine, but now define In[2]:= F[x_]:=1 and substitute this into oStatCDF In[3]:= oStatCDF[x,r,n,F] Out[3]= Indeterminate This does not look fine, since I would expect a more determinate result. Now try to help Mathematica by substituting F[x_]=1 by hand. Then F[x]^i (1-F[x])^(n-i) simplifies to 1^i 0^(n-i) == 1 In[4]:= simp[r_,n_]=Sum[Binomial[n,i] ,{i,r,n}] Out[4]= (Gamma[1+n] Hypergeometric2F1[1,-n+r,1+r,-1]) / (Gamma[1+n-r] Gamma[1+r]) Now apply simp to r = 5 and n = 100 to obtain In[5]:= simp[5,10] Out[5]= 638 Of course, 638 != Indeterminate Is this a Bug or did I make a mistake? Best regards, Johannes Ludsteck <><><><><><><><><><><><> Johannes Ludsteck Economics Department University of Regensburg Universitaetsstrasse 31 93053 Regensburg Phone +49/0941/943-2741