Description Usage Arguments Details Value References See Also Examples

Provides 1-sided or 2-sided Bayesian tolerance intervals under the conjugate prior for data distributed according to a normal distribution.

1 2 3 4 5 6 |

`x` |
A vector of data which is distributed according to a normal distribution. |

`norm.stats` |
An optional list of statistics that can be provided in-lieu of the full dataset. If provided, the user must specify all three components: the sample mean ( |

`alpha` |
The level chosen such that |

`P` |
The proportion of the population to be covered by this tolerance interval. |

`side` |
Whether a 1-sided or 2-sided tolerance interval is required (determined by |

`method` |
The method for calculating the k-factors. The k-factor for the 1-sided tolerance intervals
is performed exactly and thus is the same for the chosen method. |

`m` |
The maximum number of subintervals to be used in the |

`hyper.par` |
A list consisting of the hyperparameters for the conjugate prior: the hyperparameters for the mean ( |

Note that if one considers the non-informative prior distribution, then the Bayesian tolerance intervals are the same as the classical solution, which can be obtained by using `normtol.int`

.

`bayesnormtol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

`P` |
The proportion of the population covered by this tolerance interval. |

`x.bar` |
The sample mean. |

`1-sided.lower` |
The 1-sided lower Bayesian tolerance bound. This is given only if |

`1-sided.upper` |
The 1-sided upper Bayesian tolerance bound. This is given only if |

`2-sided.lower` |
The 2-sided lower Bayesian tolerance bound. This is given only if |

`2-sided.upper` |
The 2-sided upper Bayesian tolerance bound. This is given only if |

Aitchison, J. (1964), Bayesian Tolerance Regions, *Journal of the
Royal Statistical Society, Series B*, **26**, 161–175.

Guttman, I. (1970), *Statistical Tolerance Regions: Classical and Bayesian*,
Charles Griffin and Company.

Young, D. S., Gordon, C. M., Zhu, S., and Olin, B. D. (2016), Sample Size Determination Strategies for Normal Tolerance Intervals Using Historical Data, *Quality Engineering (to appear).*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## 95%/85% 1-sided Bayesian normal tolerance limits for
## a sample of size 100.
set.seed(100)
x <- rnorm(100)
out <- bayesnormtol.int(x = x, alpha = 0.05, P = 0.85,
side = 1, method = "EXACT",
hyper.par = list(mu.0 = 0,
sig2.0 = 1, n.0 = 10, m.0 = 10))
out
plottol(out, x, plot.type = "both", side = "upper",
x.lab = "Normal Data")
``` |

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