Re: [R] Slightly off-topic --- distribution name.
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
Re: [R] Slightly off-topic --- distribution name.
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 [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 _ David Scott Department of Statistics, Tamaki Campus The University of Auckland, PB 92019 AucklandNEW ZEALAND Phone: +64 9 373 7599 ext 86830 Fax: +64 9 373 7000 Email: [EMAIL PROTECTED] Graduate Officer, Department of Statistics __ [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