Strange statistics function integration
- To: mathgroup at smc.vnet.net
- Subject: [mg59545] Strange statistics function integration
- From: Erich Neuwirth <erich.neuwirth at univie.ac.at>
- Date: Fri, 12 Aug 2005 00:07:48 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I am experiencing some very strage effects, and in effect errors, with the continuous distributions. Here is my code <<Statistics`ContinuousDistributions` PosterioriWithNormalProb1[mu_, sigma_][n_, k_] := Binomial[n, k]*Integrate[x^k*(1 - x)^(n - k)*PDF[NormalDistribution[mu, sigma], x], {x, -Infinity,Infinity}] PosterioriWithNormalProb2[mu_,sigma_][n_,k_]:= Binomial[n,k]*Assuming[Element[ sigma1,Reals] && sigma1>0 ,Integrate[ x^k*(1-x)^(n-k)*PDF[NormalDistribution[mu1,sigma1],x],{x,- Infinity,Infinity}]]/.{mu1->mu,sigma1->sigma} The difference between these two functions seems to be that in the first case integration is done with the symbolic constants replaced by numerical values to be substituted before integration, and in the second case this substitution happens only after integration. Now, the following happens: In[78]:= PosterioriWithNormalProb1[0.5,0.1][8,0] From In[78]:= Integrate::gener: Unable to check convergence Out[78]= 0.0096998 In[79]:= PosterioriWithNormalProb2[0.5,0.1][8,0] Out[79]= 0.0096998 which seems ok. However: In[81]:= PosterioriWithNormalProb1[0.5,0.001][8,0] From In[81]:= Integrate::gener: Unable to check convergence Out[81]= 0.00780941 In[80]:= PosterioriWithNormalProb2[0.5,0.001][8,0] Out[80]= 0.00390669 In this example, the second result is correct, the first one is wrong. Since Mathematica can solve the integration problem with symbolic parameters, it is strange that the warning appears when concrete numerical paramater are used during integration. It is also strange that the problem only occurs for some values of sigma. Can anybody help me understanding what is happening here? Erich Neuwirth