[R] How to get estimate of confidence interval?

Ted Byers r.ted.byers at gmail.com
Mon Oct 20 18:50:04 CEST 2008

I thought I was finished, having gotten everything to work as intended.  This
is a model of risk, and the short term forecasts look very good, given the
data collected after the estimates are produced (this model is intended to
be executed daily, to give a continuing picture of our risk).  But now there
is a new requirement.

I have weekly samples from a non-autonomous process (i.e. although well
modelled as a decay process, with an exponential distribution fitting the
decay times well, the rate estimates and their sd vary considerably from one
week to the next).  The total number of events to be expected from a given
sample over the next week can be easily estimated from a simple integral. 
And the total number of these events from all samples, is just the sum of
these estimates over all samples.  So far, so good (imagine you have a
sample of a variety of species of radionuclides all emitting alpha particles
with the same energy - so you can't tell from the decay event which species
produced the alpha particles).

I guess there are two parts of my question.  I get a fit of the exponential
distribution to each sample using fitdistr(x,"exponential").  I am finding
the expected values vary by as much as a factor of 4, and the corresponding
estimates of sd vary by as much as a factor of 100 (some samples are MUCH
larger than others).  How do I go from the sd it gives to a 99% confidence
interval for the integral for that function from now through a week from now
(or to the end of time, or through the next month/quarter)?  And how do I
move from these estimates to get the expected value and confidence intervals
for the totals over all the samples?  I am a bit rusty on figuring out how
error propagates through model calculations (an online reference for this
would be handy, if you know of one).


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