Physicists and engineers often have to calculate the uncertainty in a derived quantity.

For instance, a test engineer repeatedly measures two separate angles. The uncertainty (or error) in the measurements of each of these angles appears to be +/- 1 degree. Subsequently, the engineer calculates the sum of these two angles. This sum is a derived quantity. But note that this derived quantity is composed of two measured quantities each having their own uncertainties, so what is the uncertainty (or error) in this derived quantity? In other words, how propagates the uncertainty from the measured quantities (the two angles) to a derived quantity (sum of two angles).

The following R code calculates the uncertainty in a derived quantity using a Monte Carlo simulation. Moreover, the Monte Carlo simulation employs copulas that fall into the *Archimedean* class of copulas. This class consists of members such as the Clayton and Gumbel copula. These Archimedean copulas make it possible to calculate the uncertainty in a derived quantity when 1) the measured quantities are dependent (correlated), and 2) the measured quantities follow a normal or some asymmetric distribution (e.g., an exponential, lognormal, or Weibull distribution).

R code that uses a *Gaussian* copula for calculating the uncertainty in a derived quantity can be found in this blog post.

Continue reading Error propagation in R: Monte Carlo simulations using copulas