stress_mean_sd {SWIM}

Stressing Mean and Standard Deviation

Description

Provides weights on simulated scenarios from a baseline stochastic model, such that stressed model components (random variables) fulfil the mean and standard deviation constraints. Scenario weights are selected by constrained minimisation of the relative entropy to the baseline model.

Usage

stress_mean_sd(
  x,
  k,
  new_means,
  new_sd,
  normalise = TRUE,
  names = NULL,
  log = FALSE,
  ...
)

Arguments

x

A vector, matrix or data frame containing realisations of random variables. Columns of x correspond to random variables; OR
A SWIM object, where x corresponds to the underlying data of the SWIM object.

k

Numeric vector, the columns of x that are stressed.

new_means

Numeric vector, same length as k, containing the stressed means.

new_sd

Numeric vector, same length as k, containing the stressed standard deviations.

normalise

Logical. If true, values of f(x) are linearly scaled to the unit interval.

names

Character vector, the names of stressed models.

log

Boolean, the option to print weights' statistics.

...

Additional arguments to be passed to nleqslv or stress_moment.

Details

The function stress_mean_sd is a wrapper for the function stress_moment. See stress_moment for details on the additional arguments to ... and the underlying algorithm.

For stressing means only, see stress_mean, for stressing higher moments and functions of moments, see stress_moment.

Value

A SWIM object containing:

• x, a data.frame containing the data;

• new_weights, a list, each component corresponds to a different stress and is a vector of scenario weights;

• type = "mean";

• specs, a list, each component corresponds to a different stress and contains k, new_means and new_sd.

See SWIM for details.

References

Pesenti SM, Millossovich P, Tsanakas A (2019). “Reverse sensitivity testing: What does it take to break the model?” European Journal of Operational Research, 274(2), 654–670.

Pesenti S BAMPTA (2020). “Scenario Weights for Importance Measurement (SWIM) - An R package for sensitivity analysis.” Annals of Actuarial Science 15.2 (2021): 458-483. Available at SSRN: https://www.ssrn.com/abstract=3515274.

Csiszar I (1975). “I-divergence geometry of probability distributions and minimization problems.” The Annals of Probability, 146–158.

See Also

Other stress functions: stress_HARA_RM_w(), stress_RM_mean_sd_w(), stress_RM_w(), stress_VaR_ES(), stress_VaR(), stress_mean_sd_w(), stress_mean_w(), stress_mean(), stress_moment(), stress_prob(), stress_user(), stress_wass(), stress()

Examples

set.seed(0)
x <- data.frame(cbind(
  "normal" = rnorm(1000),
  "gamma" = rgamma(1000, shape = 2),
  "beta" = rbeta(1000, shape1 = 2, shape2 = 2)))
## stressing mean and sd of column 1
res1 <- stress(type = "mean sd", x = x, k = 1, new_means = 0.1,
  new_sd = 1.1, method = "Newton",
  control = list(maxit = 1000, ftol = 1E-15))
summary(res1)
## calling stress_mean_sd directly
res2 <- stress_mean_sd(x = x, k = 1, new_means = 0.1,
  new_sd = 1.1, method = "Newton",
  control = list(maxit = 1000, ftol = 1E-15))

## See also examples in stress_moment.