contribution
(Package: propagate) :
Contribution to propagated uncertainty for each variable
Calculates the relative "contribution" C_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'). In the implementation here, the contributions are rescaled to sum up to 1.
fitDistr
(Package: propagate) :
Fitting distributions to observations/Monte Carlo simulations
This function fits 21 different continuous distributions by (weighted) NLS to the histogram or kernel density of the Monte Carlo simulation results as obtained by propagate or any other vector containing large-scale observations. Finally, the fits are sorted by ascending AIC.
interval
(Package: propagate) :
Uncertainty propagation based on interval arithmetics
Calculates the uncertainty of a model by using interval arithmetics based on a "combinatorial sequence grid evaluation" approach, thereby avoiding the classical dependency problem that inflates the result interval.
numDerivs
(Package: propagate) :
Functions for creating Gradient and Hessian matrices by numerical differentiation (Richardson's method) of the partial derivatives
These two functions create Gradient and Hessian matrices by Richardson's central finite difference method of the partial derivatives for any expression.
matrixStats
(Package: propagate) :
Fast column- and row-wise versions of variance coded in C++
These two functions are fast C++ versions for column- and row-wise variance calculation on matrices/data.frames and are meant to substitute the classical apply(mat, 1, var) approach.
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 and symbolic as well as evaluated versions of the Gradient and Hessian matrices. If do.sim = TRUE had been set in propagate, skewness/kurtosis and Shapiro-Wilks/Kolmogorov-Smirnov tests for normality are calculated on the Monte-Carlo evaluations.
rDistr
(Package: propagate) :
Creating random samples from a variety of useful distributions
These are random sample generators for 15 different continuous distributions which are not readily available as other Distributions in R. Some of them are implemented in other specialized packages (i.e. rsn in package 'sn' or rtrapezoid in package 'trapezoid'), but here they are collated in a way that makes them easily accessible for Monte Carlo-based uncertainty propagation.
makeDerivs
(Package: propagate) :
Utility functions for creating Gradient- and Hessian-like matrices with symbolic derivatives and evaluating them in an environment
These are three different utility functions that create matrices containing the symbolic partial derivatives of first (makeGrad) and second (makeHess) order and a function for evaluating these matrices in an environment. The evaluations of the symbolic derivatives are used within the propagate function to calculate the propagated uncertainty, but these functions may also be useful for other applications.
propagate
(Package: propagate) :
Propagation of uncertainty using higher-order Taylor expansion and Monte Carlo simulation
A general function for the calculation of uncertainty propagation by first-/second-order Taylor expansion and Monte Carlo simulation including covariances. Input data can be any symbolic/numeric differentiable expression and data based on replicates, summaries (mean & s.d.) or sampled from a distribution. Uncertainty propagation is based completely on matrix calculus accounting for full covariance structure. Monte Carlo simulation is conducted using multivariate normal or t-distributions with covariance structure.
providing 
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