# [R] Confidence Intervals for Arbitrary Functions

Jeff Newmiller jdnewmil at dcn.davis.ca.us
Sat Jul 16 19:47:51 CEST 2005

```I have a rather basic background in statistics, and am looking for
assistance in solving what I expect is a common type of problem.

I have measurements of physical processes, and mathematical models of
those processes that I want to feed the measurements into. A simple case
is using measurements of electric power entering and leaving a
power conversion device, sampled at regular intervals, and summed to
estimate energy in and out, and dividing the energy out by the energy in
to get an estimate of efficiency.  I know that power efficiency varies
with power level, but for this calculation I am interested in the
quantifying the "overall" efficiency rather than the instantaneous
efficiency.

If the energy quantities are treated as a normally-distributed random
variable (per measurement uncertainty), is there a package that simplifies
the determination of the probability distribution function for the
quotient of these values? Or, in the general sense, if I have a function
that computes a measure of interest, are such tools general enough to
handle this? (The goal being to determine a confidence interval for the
computed quantity.)

As an attempt to understand the issues, I have used SQL to generate
discrete sampled normal distributions, and then computed new abscissa
values using a function such as division and computing the joint
probability as the ordinate, and then re-partitioned the result into new
bins using GROUP BY.  This is general enough to handle non-normal
distributions as well, though I don't know how to quantify the numerical
stability/accuracy of this computational procedure. However, this is
pretty tedious... it seems like R ought to have some straightforward
solution to this problem, but I don't seem to know what search terms to
use.

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