The Stoppa distribution

Try the following, which have the usual lower.tail and log.p arguments to make
it easier to get accurate results in the tails.  logspace_sub() is an R version of
the R C-API function Rf_logspace_sub().  I haven't tested the [pq]stoppa functions
much.

logspace_sub <- function (logx, logy)
{
    # log(exp(logx) - exp(logy)), avoiding unnecessary floating point error
    dxy <- logx - logy
    # log(2) looks like best breakpoint
    logx + ifelse(dxy < 0.693147180559945, log(-expm1(-dxy)), log1p(-exp(-dxy)))
}

pstoppa <- function(q, y0, alpha, theta = 1, lower.tail = TRUE, log.p = FALSE)
{
    logp <- theta * logspace_sub(0, -alpha * log(q/y0))
    if (!lower.tail) {
        logp <- logspace_sub(0, logp)
    }
    if (log.p) logp else exp(logp)
}

qstoppa <- function(p, y0, alpha, theta = 1, lower.tail = TRUE, log.p = FALSE)
{
    logp <- if (log.p) {
                if (lower.tail) p else logspace_sub(0, p)
            } else {
                if (lower.tail) log(p) else log1p(-p)
            }
    logq <- log(y0) - 1/alpha * logspace_sub(0, logp/theta)
    exp(logq)
}

Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf
Of Andrew Hoerner
Sent: Friday, December 13, 2013 4:13 PM
To: r-help
Subject: [R] The Stoppa distribution

The Stoppa distribution is a 3-parameter distribution that generalizes the
Pareto distribution, adding a second shape parameter but no location term.
The CDF is

                                    F(x) =  [1-(x/x0)-?]?    0 < x0 < x

Kleiber & Kotz (2003). *Statistical Size Distributions in Economics and
Actuarial Sciences.*    I do not believe that the Stoppa distribution has
been implemented in R under that name.


Does anyone know if the Stoppa distribution has been implimented in R under
a different name, or if there is a more generalized distribution containing
the Stoppa as a special case which has been implemented in R? (The
generalized beta of the second kind, maybe?) And if so, how you need to set
the parameters of the more general distribution to collapse it to the
Stoppa?

Any help anyone could offer would be greatly appreciated.

Sincerely, andrewH

	[[alternative HTML version deleted]]