Re: propagation of uncertainty from heterogeneous distributions

Robert Dodier wrote:
> Chris Chiasson wrote:
>
>> http://physics.nist.gov/Pubs/guidelines/appa.html gives a method
for
>> propagating uncertainty and
>> http://physics.nist.gov/cuu/Uncertainty/typeb.html gives a method
for
>> converting various sources into standard uncertainties.
>
> What's described there are some approximations for special cases.
>
>> But I need to know, if distributions are of different types, what
is
>> the method for determining the coverage (confidence level??) of the
>> propagated uncertainty?
>
> The general method to find the distribution of a function of
> some variables for which the pdf's are known is
> the change of variable theorem, which is described in standard
> texts, e.g. Hogg and Craig, Introduction to Mathematical Statistics.
> In special cases, other methods might also yield exact results.
>
> By the way, forget about "confidence levels". What you want
> is a probability distribution (described equivalently by the pdf or
> cdf).
>
>> A (possibly) related question is, how can one determine the PDF of
>> the subtraction (as an example math operation) of two heterogeneous
>> distributions (say triangular and normal)?
>
> Assuming independence, the pdf of X minus Y is the convolution
> of the pdf of X with the reflection of the pdf of Y about Y = 0.
>
>> What about other operations?
>
> It is not too difficult to state a general solution in terms of
> the change of variable theorem. However, there may well
> be no "nice" results for some combinations of distributions
> and operations. Sums are nice, but products and ratios
> generally aren't.
>
> For what it's worth,
> Robert Dodier

.... the pages do seem to be looking for answers of the "formula"
type and don't seem to consider (from a brief glance) providing an
answer in the form of a set of random numbers representing the
uncertainty. Answers of this type are relatively easy to obtain, since
you just simulate all the components, dependencies etc. and combine
them to create a final set of random numbers.

David Jones


.

Relevant Pages