I think you're confusing this with the correct result that (X+Y)/(X-Y) has
a Cauchy distribution - Peter M Lee

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On Tue, 17 Feb 2004, Jeppe H. Rich wrote:

> >From somewhere deep down in my memory, I have the idea that if X and Y
> are normal then Z=X/Y will be Cauchy distributed. Please do not take
> this for granted but check out. Of course, as Phillip points out you
> should be careful with the domains here.
>
> A second thing, why not use log-normal distributions in your simulation?
> They are invariant to inversion.
>
> /Jep
>
> ----------------------------------
> Jeppe Husted Rich, MSc, PhD
> Assistant Professor
> Technical University of Denmark
> Centre for Traffic and Transport
> Building 115, 2800 Lyngby Denmark
> Work: +45 45251536
> Privat: +45 36308595
> Fax: +45 45936412
> E-mail: [log in to unmask]
> Skype account: jeppe.husted.rich
> ----------------------------------
>
> -----Original Message-----
> From: Phillip Good [mailto:[log in to unmask]]
> Sent: 17. februar 2004 15:36
> To: [log in to unmask]
> Subject: Re: distribution of 1/X , if X belongs to a normal distribution
>
> Yes, but what if none of the moments exist as in the present case?
>
> Phillip Good
>
> ----- Original Message -----
> From: Osher Doctorow PhD <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Monday, February 16, 2004 11:52 PM
> Subject: Re: distribution of 1/X , if X belongs to a normal distribution
>
>
> > >From Osher Doctorow [log in to unmask]
> >
> > If Y is a function of random variable X, then under rather general
> > conditions if fX(x) is the probability density function (pdf) of X
> > for X continuous and if fY(y) is the pdf of Y for Y continuous, then:
> >
> > 1) fY(y) = fX(x(y))x'(y)
> >
> > where x'(y) is dx/dy evaluated at x(y) (the inverse of Y as a function
> > of X all in terms of y rather than x).
> >
> > Rather than solve your particular problem, I'll give an example from
> > Paul G. Hoel, S. C. Port, and C. J. Stone, Introduction to Probability
> > Theory, Houghton-Mifflin: Boston 1971, pp. 120-121. Let X be exponent-
> > ially distributed with parameter L, so that fX(x) = Lexp(-Lx) for
> > L > 0 and 0 elsewhere.  Find the pdf of Y = X^(1/b) where ^ indicates
> > exponent.  Since Y = X^(1/b), write y = x^(1/b), so x = y^b, and dy/dx
> > = by^(b-1).  Also, fX(x(y)) is fX(x) with x replaced by whatever
> > function of y it is, or here x = y^b, so fX(x(y)) = Lexp(-Ly^b). Both
> > factors are now functions of y, so just multiply them together as in
> > equation (1) to get the answer when y > 0 (the density is 0 other-
> > wise).  Remember to take /fX(x(y))/, though.
> >
> > Osher Doctorow
> > > Dear All,
> > >     I am an engineer, so please forgive me if my post seems to be
> naive.
> > >     I am currently considering  a very common structural problem. In
> > > order to predict the behaviour of the response, I simulate the
> system
> > > using a Monte Carlo method. Without going into too much unecessary
> > > detail, I am considering a system where the X random variable
> follows
> > > the  Normal distribution ( X~N(\mu_X, \sigma_X) ), and another
> random
> > > variable Y is related to X with the following formula
> > >     Y= c/X,
> > > where c is a constant.
> > >     As I said earlier, I am simulating this system and the
> distribution
> > > I am receiving for Y is not Normal (of course for low ratios of
> > > (\sigma_X / \mu_X)  it can be approximated by the normal
> distribution ),
> > > and is skewed. At this point, I am trying to avoid reinventing the
> wheel
> > > by trying to determine whether Y follows a formal statistical
> > > distribution that I am not aware of. (I am aware of the inverse
> normal
> > > distribution, but  I was led to believe that it is not suitable in
> this
> >
> > > situation).
> > >     So I would appreciate it if you could provide me with
> information
> > > regarding the distribution that Y is following, if it follows one.
> > > Also, if you could point me towards any publications that you feel
> are
> > > relevant I would appreciate it.
> > >     Thank you in advance.
> > >
> > > Kind regards
> > > Nikos Papadakis
> > >
> > > --
> > > Dr Nikolaos Papadakis
> > > Research Fellow
> > > IARC 4th Floor,
> > > University of Warwick,
> > > Gibbet Hill Road
> > > Coventry CV4 7AL
> > > tel: +44-2476 523684
> > > fax: +44-2476 523387
> >
>
>