tolerance (version 0.4.0)

mvtol.region: Multivariate Normal Tolerance Regions

Description

Determines the appropriate tolerance factor for computing multivariate normal tolerance regions based on Monte Carlo simulation.

Usage

mvtol.region(x, alpha = 0.05, P = 0.99, B = 1000)

Arguments

x

An nxp matrix of data assumed to be drawn from a p-dimensional multivariate normal distribution. n pertains to the sample size.

alpha

The level chosen such that 1-alpha is the confidence level. A vector of alpha values may be specified.

P

The proportion of the population to be covered by this tolerance region. A vector P values may be specified.

B

The number of iterations used for the Monte Carlo algorithm which determines the tolerance factor. The number of iterations should be at least as large as the default value of 1000.

Value

• mvtol.region returns a matrix where the rows pertain to each confidence level 1-alpha specified and the columns pertain to each proportion level P specified.

Details

A basic sketch of how the algorithm works is as follows: (1) Generate independent chi-square random variables and Wishart random matrices. (2) Compute the eigenvalues of the randomly generated Wishart matrices. (3) Iterate the above steps to generate a set of B sample values such that the 100(1-alpha)-th percentile is an approximate tolerance factor.

References

Krishnamoorthy, K. and Mondal, S. (2006), Improved Tolerance Factors for Multivariate Normal Distributions, Communications in Statistics - Simulation and Computation, 35, 461--478.

Examples

## 90\%/90\% bivariate normal tolerance region. 

set.seed(100)
x1 <- rnorm(100, 0, 0.2)
x2 <- rnorm(100, 0, 0.5)
x <- cbind(x1, x2)

out1 <- mvtol.region(x = x, alpha = 0.10, P = 0.90, B = 1000)
out1
plottol(out1, x)

## 90\%/90\% trivariate normal tolerance region. 

set.seed(100)
x1 <- rnorm(100, 0, 0.2)
x2 <- rnorm(100, 0, 0.5)
x3 <- rnorm(100, 5, 1)
x <- cbind(x1, x2, x3)
mvtol.region(x = x, alpha = c(0.10, 0.05, 0.01), 
             P = c(0.90, 0.95, 0.99), B = 1000) 

out2 <- mvtol.region(x = x, alpha = 0.10, P = 0.90, B = 1000) 
out2
plottol(out2, x)