[R] Confidence Intervals for Arbitrary Functions

[Gabor Grothendieck]

On 7/16/05, Jeff Newmiller <jdnewmil at dcn.davis.ca.us> wrote:
> 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.
> 

There is some discussion about the ratio of normals at:

   http://www.pitt.edu/~wpilib/statfaq.html

but you may just want to use bootstrapping:

  library(boot)
  library(simpleboot)