Estimates from Monte Carlo Simulation

Usage

# S3 method for class 'MCS_log'
summary(object, unit = NULL, ...)

# S3 method for class 'MCS'
summary(object, unit = NULL, ...)

Arguments

object: numeric vector of class "MCS" or "MCS_log". The values from n Monte Carlo Simulations
unit: (optional) object of class units or symbolic_units, or in the case of set_units expression with symbols.
...: additional arguments affecting the summary produced.

Value

a list. If class of object is "MCS", the list contains the following elements:

median: median of the Monte Carlo simulations
ir.95: the 95% and 68% interpercentile range
ir.68: the 68% interpercentile range
mean: arithmetic mean the Monte Carlo simulations
sd: 1\(\sigma\) standard deviation
conf.int: 95% confidence intverval about the mean
stderr: standard error
t.test: Statistic and p-value of the Student's t-test
n: Number of samples

If class of object is "MCS_log", the list contains the following elements:

median: median of the Monte Carlo simulations
ir.95: the 95% and 68% interpercentile range
ir.68: the 68% interpercentile range
mean: geometric mean the Monte Carlo simulations
sd: 1\(\sigma\) range about the mean
sd2: 2\(\sigma\) range about the mean
conf.int: 95% confidence intverval about the mean
stderr.log: standard error of log(samples)
t.test: Statistic and p-value of the Student's t-test of log(samples)
n: Number of samples

Values will be in the unit specified by parameter unit or be equal to the unit of x if x is a units object.

Details

Equations of the form \(X = A b^{n \pm \sigma}\) create non-normal, left-skewed distributions (e.g. flow laws, and grain-size piezometers). Thus, it is recommended to report median and percentiles instead of mean, standard deviation and confidence intervals.

Examples

set.seed(20250411)
MC_res <- grainsize_piezometry(12.2)
summary(MC_res)
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      92 MPa 
#> 95% interpercentile range:   49 - 190 MPa 
#> Standard error in log-space: 0.000151644
#> Student's t-Test:            p<0.05

n <- 100
temperature <- units::set_units(rnorm(n, 300, 25), degC)
pressure <- units::set_units(rnorm(n, 400, 50), MPa)
MC_res2 <- ps_fugacity(pressure, temperature) # 37 MPa
summary(MC_res2)
#> Statistical summary of 100 Monte Carlo simulations
#> 
#> Mean:                    390 bar 
#> 95% confidence interval: 370 - 420 bar 
#> Standard error:          11.9467
#> Student's t-Test:        p<0.05