Re: Integrate Problems
- To: mathgroup at smc.vnet.net
- Subject: [mg22378] Re: [mg22350] Integrate Problems
- From: BobHanlon at aol.com
- Date: Sat, 26 Feb 2000 22:05:05 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
The following is for version 3 Since you are working with a distribution, make use of the standard add-on packages Needs["Statistics`NormalDistribution`"] PDF[NormalDistribution[a, b], x] 1/(E^((-a + x)^2/(2*b^2))*b*Sqrt[2*Pi]) Integrating from -Infinity to Infinity. Symbolically: Limit[CDF[NormalDistribution[a, b], a+n*b], n -> Infinity] 1 or, with a change in variable, t = (x-a)/b CDF[NormalDistribution[0, 1], Infinity] 1 For the specific distribution: CDF[NormalDistribution[40000, 4000], Infinity] 1 Integrating from -Infinity to zero CDF[NormalDistribution[a, b], 0] (1 - Erf[a/(Sqrt[2]*b)])/2 CDF[NormalDistribution[40000, 4000], 0] 1/2*(1 - Erf[5*Sqrt[2]]) %//N 0. Integrating from -Infinity to the mean CDF[NormalDistribution[a, b], a] 1/2 Integrals from 0 to Infinity would be (1- CDF[NormalDistribution[a, b], 0])//Simplify 1/2*(1 + Erf[a/(Sqrt[2]*b)]) (1- CDF[NormalDistribution[40000, 4000], 0])//Simplify 1/2*(1 + Erf[5*Sqrt[2]]) %//N 1. Bob Hanlon In a message dated 2/25/2000 10:59:59 PM, com3 at ix.netcom.com writes: >Can someone provide some help with the following results I get from >version 3 ? > >a=40000 >b=4000 >f[x_]:=(1/(b*(2*Pi)^.5))*Exp[(-1/2)*((x-a)/b)^2] > >Integrate[f[x],{x,-Infinity,+Infinity}] >Returns the correct value of 1. > >NIntegrate[f[x],{x,-Infinity,+Infinity}] >Returns a somewhat correct value of 1.00121 > >Integrate[f[x],{x,-Infinity,0}] >Returns a "System`$$Failure" term > >NIntegrate[f[x],{x,-Infinity,0}] >Returns a 7.6E-24 which is incorrect > >Integrate[f[x],{x,0,+Infinity}] >Returns a "System`$$Failure" term > >NIntegrate[f[x],{x,0,+Infinity}] >Returns an incorrect value of 1.00121 > >I need to obtain numerical values from these and similar calculations >and suspect that some options need to be changed. Symbolic solutions >would be preferred if possible. Are there guidelines that can help >define what options for Integrate/NIntegrate work best ? >