Tim Hesterberg has pointed out to me that the interpretation
"For rate < 0 consider this as the distribution of
-X where X ~ gamma(-rate, shape)"
does not work for dgamma() and pgamma().
The use of dgamma() with a negative rate parameter gives negative values for
the density. A density function is always non-negative. Furthermore we have
the following result:
Let X~gamma(shape,-rate) with rate<0. Let f denote a density function for
X and let g denote a density function for -X, then g(x) = f(-x).
The use of pgamma() with rate<0 gives a decreasing cumulative distribution
function. A distribution function is always nondecreasing. Furthermore we
have the following result:
Let X~gamma(shape,-rate) with rate<0. Let F denote the cdf for X and let G
denote the cdf for -X, then G(x) = 1-F(-x).
These problems in the functions could of course be corrected but I really
think that the build-in functions related to the
gamma(rate,shape)-distribution should observe the restrictions rate>0 and
shape>0. This would not exclude the possibility of making transformations of
gamma-distributed variables but make sure that we really wanted to make a
transformation.
Leslie.
-----------------------------------------
Leslie Foldager
ConStat
The North Sea Centre
P.O. Box 104
DK-9850 Hirtshals
Denmark
Tel: +45 98 94 35 52
Fax: +45 98 94 48 33
E-mail: leslie@constat.dk
WEB: www.constat.dk
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