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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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)