I would have thought this to be relatively elementary, but I can't find it
mentioned in any of my stats texts.
Please consider the following:
library(fitdistrplus)
fp = fitdist(y,"exp");
rate = fp$estimate;
sd = fp$sd
fOneWeek = exp(-rate*7); #fraction that happens within a week - y is
measured in days
fr = exp(-rate*dt); #fraction remaining - dt = elapsed time from time of
sample to present
fh = 1 - fr; # fraction that occurred from time of sample to present
# assume n = total number that have happened from time of sample to present
T = n / fh # t is the total number at y = 0
NR = fr * T
NNW = NR * (1 - fOneWeek)
(If you wanted to run this, just populate y with random numbers from an
exponential distribution.)
What I show here simply extracts an estimate and standard deviation from the
data.frame returned by fitdist, and tries to compute a number of integrals.
What I need is the number of events that can be expected next week, next
month, and from now to the end of time. Unless I have gone senile in my old
age, I have the integrals correct. Please correct me if I missed something.
But what I need help (to refresh my memory - I used to know this way back in
the stone age) to compute the confidence intervals for each of these
integrals.
So I don't bother anyone with similar elementary questions, what web
resource exists that defines confidence intervals for such integrals for
arbitrary distributions? or does such a resource exist?
Thanks
Ted
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