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. :-)
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