getSTB {STB}

Load/unload C-lib. Simultaneous Tolerance Bands Using R-Implementation.

Description

Compute simultaneous tolerance bounds (STB) from a matrix.

Usage

getSTB(
  mat,
  alpha = 0.05,
  tol = 1e-04,
  max.iter = 100L,
  q.type = 2L,
  logfile = NULL,
  output = TRUE,
  timer = FALSE,
  Ncpu = 2
)

Arguments

mat

(numeric) matrix with nrow=N_simulation, ncol=N_points, where each row is sorted in increasing order

alpha

(numeric) 100(1-alpha)% simultaneous tolerance-level will be computed

tol

(numeric) value controlling the termination of the bisection algorithm, i.e. the condition coverage-(1-alpha)<=tol has to be TRUE.

max.iter

(integer) maximum number of iterations of the bisection algorithm. If this number is reached the algorithm terminates and returns the best approximation of lower and upper bounds reached up to this iteration.

q.type

(integer) the quantile-type used if algo="R", see ? quantile for details.

logfile

(character) string specifying the name of the (optional) log-file, storing the iteration history

output

(logical) TRUE a txtProgressBar will be printed as well as additional status information

timer

(logical) TRUE = the time spent for computing the STB will be printed

Ncpu

(integer) specifying the number cores/CPUs to be used in computing the coverage on C-level, for N>1 multi-processing is applied

Details

Function computes 100(1-alpha)% simultaneous tolerance bounds (intervals, bands) from a matrix, where rows correspond to order statistics (sorted) of random samples of a, e.g. normal distribution. It starts by computing joint coverage of the naive unadjusted (point-wise) alpha-level intervals, computed as percentiles across each order statistic (columns). Alpha is decreased using a bisection search until the joint coverage becomes at least 100(1-alpha)% depending on arguments max.iter and tol. If the number of simulated random samples goes to infinity, the STB becomes exact. Note that checking whether a numeric vector is normally distributed is equal to checking whether the residuals of the simplest linear model y = mu + e (y~1) are normally distributed [e ~ N(0, sigma^2)].

Value

(list) with elements:

Q

(numeric) matrix with two rows, where the 1st row = lower bounds of the STB, 2nd row = upper bounds of the STB

cov

(numeric) value indicating the actual coverage of the STB

Author(s)

Andre Schuetzenmeister [e-mail]

References

Schuetzenmeister, A., Jensen, U., Piepho, H.P. (2011), Checking assumptions of normality and homoscedasticity in the general linear model. Communications in Statistics - Simulation and Computation; S. 141-154

See Also

fastSTB stb

Examples

## Not run: 
set.seed(333)
mat <- t(apply(matrix(rnorm(10000*30), ncol=30), 1, sort))
stb.obj <- getSTB(mat, timer=TRUE)
stb.obj$cov

## End(Not run)