Re: How to express the results in normal cdf instead of erf()
- To: mathgroup at smc.vnet.net
- Subject: [mg97133] Re: How to express the results in normal cdf instead of erf()
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 6 Mar 2009 04:24:09 -0500 (EST)
- Organization: Uni Leipzig
- References: <goo7jt$sga$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi, res = Integrate[PDF[NormalDistribution[0, 1], x] Exp[x], x]; and res /. Erf[a_] :> Erf[Expand[a]] /. RuleDelayed @@ Reverse[((2* # - 1) & /@ {cdf[NormalDistribution[0, 1], a*x + b], 1/2*(1 + Erf[a_.*x/Sqrt[2] + b_.])} /. x -> Sqrt[2]*y) /. y -> x] you must use cdf[] instead of CDF[] because otherwise Mathematica will evaluate it back to Erf[] Regards Jens Irving Zhu wrote: > Hi All, > > I am working on some integrals involving the Normal Distribution, and would > like the end results to be expressed in normal density as opposed to the > Erf[] function. > > For example, the default result of the following: > > Integrate[PDF[NormalDistribution[0, 1], x] Exp[x], x] will result in an > expression in Erf[]. > > I'd like it to be in terms of CDF[NormalDistribution[]] instead. > > Of course the two functions are related: > > CDF[NormalDistribution[0,1],x] ==1/2*(1+Erf[[x/Sqrt[2]]) > > > Is there any way to do that? > > Thanks, > Irving. > >