[R] OT: distribution of a pathological random variate

(Ted Harding) Ted.Harding at manchester.ac.uk
Wed Aug 29 20:02:34 CEST 2007

On 29-Aug-07 17:39:17, Horace Tso wrote:
> Folks,
> I wonder if anything could be said about the distribution of a random
> variate x, where
> x = N(0,1)/N(0,1)
> Obviously x is pathological because it could be 0/0. If we exclude this
> point, so the set is {x/(0/0)}, does x have a well defined
> distribution? or does it exist a distribution that approximates x. 
> (The case could be generalized of course to N(mu1, sigma1)/N(mu2,
> sigma2) and one still couldn't get away from the singularity.)
> Any insight or reference to related discussion is appreciated.
> Horace Tso

A good question -- but it has a long-established answer. X has the
Cauchy distribution, whose density function is

  f(x) = 1/(pi*(1 + x^2))

Have a look at ?dcauchy

It is also the distribution of t with 1 degree of freedom.

See also ?dt

You don;t need to exclude the point (0,0) explicitly, since
it has zero probabilityof occurring. But the chance that the
denominator could be small enough to give a very large value
of X is quite perceptible.



and similar. Play around!

Best wishes,

E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 29-Aug-07                                       Time: 19:02:32
------------------------------ XFMail ------------------------------

More information about the R-help mailing list