Description Usage Arguments Value References See Also Examples

Provides depth-based multivariate central or semi-space nonparametric tolerance regions. These can be calculated for any continuous multivariate data set. Either (P, 1-alpha) tolerance regions or beta-expectation tolerance regions can be specified.

1 2 3 4 5 |

`x` |
An |

`alpha` |
The level chosen such that |

`P` |
The proportion of the population to be covered by this tolerance interval. Note that if a (P, 1-alpha) tolerance region is required, then both |

`Beta` |
The confidence level for a beta-expectation tolerance region. Note that if a beta-expectation tolerance region is required, then |

`depth.fn` |
The data depth function used to perform the ordering of the multivariate data. Thus function must be coded in such a way that the first argument is multivariate data for which to calculate the depth values and the second argument is the original multivariate sample, |

`adjust` |
Whether an adjustment should be made during an intermediate calculation for determining the number of points that need to be included in the multivariate region. If |

`type` |
The type of multivariate hyperrectangular region to calculate. If |

`semi.order` |
If |

`L` |
If |

`U` |
If |

`...` |
Additional arguments passed to the |

`npmvtol.region`

returns a `p`

x`2`

matrix where the columns give the lower and upper limits, respectively, of the multivariate hyperrectangular tolerance region.

Young, D. S. and Mathew, T. (2020+), Nonparametric Hyperrectangular Tolerance
and Prediction Regions for Setting Multivariate Reference Regions in Laboratory
Medicine, *Submitted*.

`distfree.est`

, `mvtol.region`

, `npregtol.int`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
## 90%/95% semi-space tolerance region for a sample
## of size 20 generated from a multivariate normal
## distribution. The mdepth function below is not
## a true depth function, but used only for
## illustrative purposes.
mdepth <- function(pts, x){
mahalanobis(pts, center = rep(0, 3),
cov = diag(1, 3))
}
set.seed(100)
x <- cbind(rnorm(100), rnorm(100), rnorm(100))
out <-npmvtol.region(x = x, alpha = 0.10, P = 0.95, depth.fn = mdepth,
type = "semispace", semi.order = list(lower = 2,
center = 3, upper = 1))
out
``` |

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