Integration of function fails

• To: mathgroup at smc.vnet.net
• Subject: [mg57866] Integration of function fails
• From: "Janssen, M.P." <M.P.Janssen at umcutrecht.nl>
• Date: Fri, 10 Jun 2005 02:29:46 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I tried to integrate the formula below and found that it converges
(numerically that is) but the analytical evaluation seems to be instable.
Is there an alternative option for evaluation or maybe an approximation?

Regards,

Mart

PS the code takes quite some time to produce the plots!

<<Statistics`NormalDistribution`
ndist=NormalDistribution[0,1]
Npart[t_]:=2^(t/d);Nprob[t_]:=1-CDF[ndist,fact
Log[Npart[t]/ps/X50]/Log[X95/X50]];
Cumparts[x_]:=Integrate[Npart[t]Nprob[t],{t,0,x},Assumptions->{X50
\[Element] Reals,X95 \[Element] Reals, ps \[Element] Reals, d \[Element]/ Reals, X50>0, X95>0, ps>0,
d>0}];
NCumparts[x_]:=NIntegrate[Npart[t]Nprob[t],{t,0,x}];
d=.2;ps=1;X95=2400;X50=X95/3; fact=Quantile[ndist,0.95];
Plot[{Cumparts[t],.75 * NCumparts[t]},{t,.03,10},PlotRange->All]
Plot[Cumparts[t],{t,.03,15},PlotRange->All]
Plot[ NCumparts[t],{t,.03,15},PlotRange->All]
NCumparts[%]
Clear[X50, X95, ps, d];
Cumparts[%]

**Output: Integrate::gener: Unable to check convergence.

```

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