summary.propagate {propagate}

Summary function for 'propagate' objects

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

## 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}\left(\frac{\partial f}{\partial x_i}\right)

The "contribution" matrix is then \mathbf{C} = \mathbf{SS}^T\mathbf{\Sigma}, where \mathbf{\Sigma} 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

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)