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

A.J. Rossini rossini at blindglobe.net
Wed Sep 15 20:38:08 CEST 2004

```Have you checked Johnson and Kotz?  That's the obvious place to start
looking for distributions beyond the usual.

Rolf Turner <rolf at math.unb.ca> writes:

> 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. :-)
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
>

--
Anthony Rossini			    Research Associate Professor
rossini at u.washington.edu            http://www.analytics.washington.edu/
Biomedical and Health Informatics   University of Washington
Biostatistics, SCHARP/HVTN          Fred Hutchinson Cancer Research Center
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