Re: Another Integrate error
- To: mathgroup at smc.vnet.net
- Subject: [mg52604] Re: Another Integrate error
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Fri, 3 Dec 2004 03:54:51 -0500 (EST)
- References: <comgts$9gn$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Ray Koopman wrote:
> This is a bivariate normal probability density:
>
> In[1]:= f[x_,y_,r_] = Exp[(x^2 + y^2 - 2*r*x*y)/(r^2 - 1)] /
> (Pi Sqrt[1 - r^2]);
>
> It should integrate to 1:
>
> In[2]:= Integrate[f[x,y,r],{x,-Infinity,Infinity},{y,-Infinity,Infinity}]
> Out[2]= 0
>
> In[3]:= Integrate[f[x,y,r],{x,-Infinity,Infinity},{y,-Infinity,Infinity},
> Assumptions -> {Element[r,Reals], -1 < r < 1}]
> Out[3]= 1
>
> In this case I happened to know that the integal should be 1,
> but what about more obscure cases?
> When can I believe a result from Integrate?
>
> In[4]:= $Version
> Out[4]= 5.0 for Mac OS X (November 19, 2003)
>
Hi,
This looks like the same bug that Vivien Lecomte reported a short while
ago. It has gone at 5.1.
I guess you have to accept that all software has bugs - including the
stuff they use to manage air traffic control - and in my experience
Mathematica has less bugs than most. If a result is important to you -
or seems unlikely - it is always worth cheching it another way - such as
doing the double integral in two steps, or using NIntegrate for one or
two randomly chosen values of r.
David Bailey