# summary.propagate: Summary function for 'propagate' objects In propagate: Propagation of Uncertainty

## Description

Provides a printed summary of the results obtained by propagate, such as statistics of the first/second-order uncertainty propagation, Monte Carlo simulation, the covariance matrix, symbolic as well as evaluated versions of the Gradient ("sensitivity") and Hessian matrices, relative contributions, the coverage factor and the Welch-Satterthwaite degrees of freedom. If do.sim = TRUE was set in propagate, skewness/kurtosis and Shapiro-Wilks/Kolmogorov-Smirnov tests for normality are calculated on the Monte-Carlo evaluations.

## Usage

 1 2 ## S3 method for class 'propagate' summary(object, ...) 

## Arguments

 object an object returned from propagate. ... other parameters for future methods.

## Details

Calculates the "sensitivity"" S_i of each variable x_i to the propagated uncertainty, as defined in the Expression of the Uncertainty of Measurement in Calibration, Eqn 4.2, page 9 (see 'References'):

S_i = \mathrm{eval}≤ft(\frac{\partial f}{\partial x_i}\right)

The "contribution" matrix is then \mathbf{C} = \mathbf{SS}^T\mathbf{Σ}, where \mathbf{Σ} is the covariance matrix. In the implementation here, the "relative contribution" matrix \mathbf{C}_{\mathrm{rel}} is rescaled to sum up to 1.

## Value

A printed output with the items listed in 'Description'.

## Author(s)

Andrej-Nikolai Spiess

## References

Expression of the Uncertainty of Measurement in Calibration.
European Cooperation for Accreditation (EA-4/02), 1999.

## Examples

 1 2 3 4 5 6 7 EXPR1 <- expression(x^2 * sin(y)) x <- c(5, 0.01) y <- c(1, 0.01) DF1 <- cbind(x, y) RES1 <- propagate(expr = EXPR1, data = DF1, type = "stat", do.sim = TRUE, verbose = TRUE, nsim = 100000) summary(RES1) 

propagate documentation built on May 7, 2018, 1:03 a.m.