Have you checked Johnson and Kotz? That's the obvious place to start looking for distributions beyond the usual.
Rolf Turner <[EMAIL PROTECTED]> 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 > [EMAIL PROTECTED] > > 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. :-) > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > -- Anthony Rossini Research Associate Professor [EMAIL PROTECTED] http://www.analytics.washington.edu/ Biomedical and Health Informatics University of Washington Biostatistics, SCHARP/HVTN Fred Hutchinson Cancer Research Center UW (Tu/Th/F): 206-616-7630 FAX=206-543-3461 | Voicemail is unreliable FHCRC (M/W): 206-667-7025 FAX=206-667-4812 | use Email CONFIDENTIALITY NOTICE: This e-mail message and any attachme...{{dropped}} ______________________________________________ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html