# [R] Slightly off-topic --- distribution name.

Rolf Turner rolf at math.unb.ca
Wed Sep 15 20:28:32 CEST 2004

```I've built R functions to ``effect'' a particular distribution, and
would like to find out if that distribution is already ``known'' by
an existing name.  (I.e. suppose it were called the ``Melvin''
distribution --- I've built dmelvin, pmelvin, qmelvin, and rmelvin as
it were, but I need a real name to substitute for melvin.)

The distribution is really just a toy --- but it provides a nice (and
``non-obviouse'') example of a two parameter distribution where both
the moment and maximum likelihood equations for the parameter
estimators are readily solvable, but at the same time are
``interesting''.  So it's good for exercises in an intro math-stats
course.

The distribution is simply that of the ***difference*** of two
independent exponential variates, with different parameters.

I.e.  X = U - V  where U ~ exp(beta) and V ~ exp(alpha) (where
E(U) = beta, E(V) = alpha).

This makes the distribution of X something like an asymetric Laplace
distribution, with its mode at 0.  (One could shift the mode too, but
that would add a third parameter, which would be de trop.)

Anyhow:  Is this a ``known'' distribution?  Does it have a name?
(I've never seen it mentioned in any of the intro math-stat books
that I've looked into.) If not, can anyone suggest a good name for
it?  (Don't be rude now!)

cheers,

Rolf Turner
rolf at math.unb.ca

P. S.  To save you putting pen to paper and working it out,
the density function is

{ exp(x/alpha)/(alpha + beta) for x <= 0
f(x) = {
{ exp(-x/beta)/(alpha + beta) for x >= 0

The mean and variance are mu = beta - alpha and
sigma^2 = alpha^2 + beta^2 respectfully. :-)

```