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. :-)
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 > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >-- 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 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}}
I believe this is the skew-Laplace distribution, although the skew-Laplace does allow for the location of the mode of the distribution to vary. Have a look at the function dskewlap in HyperbolicDist. The help on that function gives a reference to a paper by Feiller et al which describes the distribution. David Scott On Wed, 15 Sep 2004, Rolf Turner wrote:> > 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 > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >_________________________________________________________________ David Scott Department of Statistics, Tamaki Campus The University of Auckland, PB 92019 Auckland NEW ZEALAND Phone: +64 9 373 7599 ext 86830 Fax: +64 9 373 7000 Email: d.scott at auckland.ac.nz Graduate Officer, Department of Statistics