Description Usage Arguments Details Value Note References See Also Examples

Provides 1-sided or 2-sided tolerance intervals for negative binomial random variables. From a statistical quality control perspective, these limits use the number of failures that occur to reach `n`

successes to bound the number of failures for a specified amount of future successes (`m`

).

1 2 3 | ```
negbintol.int(x, n, m = NULL, alpha = 0.05, P = 0.99,
side = 1, method = c("LS", "WU", "CB",
"CS", "SC", "LR", "SP", "CC"))
``` |

`x` |
The total number of failures that occur from a sample of size |

`n` |
The target number of successes (sometimes called size) for each trial. |

`m` |
The target number of successes in a future lot for which the tolerance limits will be calculated. If |

`alpha` |
The level chosen such that |

`P` |
The proportion of the defective (or acceptable) units in future samples of size |

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

`method` |
The method for calculating the lower and upper confidence bounds, which are used in the calculation
of the tolerance bounds. The default method is |

This function takes the approach for Poisson and binomial random variables developed in Hahn and Chandra (1981) and applies it to the negative binomial case.

`negbintol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

`P` |
The proportion of defective (or acceptable) units in future samples of size |

`pi.hat` |
The probability of success in each trial, calculated by |

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

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

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

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

Recall that the geometric distribution is the negative binomial distribution where the size is 1. Therefore, the case when `n = m = 1`

will provide tolerance limits for a geometric distribution.

Casella, G. and Berger, R. L. (1990), *Statistical Inference*, Duxbury Press.

Hahn, G. J. and Chandra, R. (1981), Tolerance Intervals for Poisson and Binomial Variables,
*Journal of Quality Technology*, **13**, 100–110.

Tian, M., Tang, M. L., Ng, H. K. T., and Chan, P. S. (2009), A Comparative Study of Confidence Intervals for Negative Binomial Proportions,
*Journal of Statistical Computation and Simulation*, **79**, 241–249.

Young, D. S. (2014), A Procedure for Approximate Negative Binomial Tolerance Intervals, *Journal of Statistical Computation and Simulation*, **84**, 438–450.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## Comparison of 95%/99% 1-sided tolerance limits with
## 50 failures before 10 successes are reached.
negbintol.int(x = 50, n = 10, side = 1, method = "LS")
negbintol.int(x = 50, n = 10, side = 1, method = "WU")
negbintol.int(x = 50, n = 10, side = 1, method = "CB")
negbintol.int(x = 50, n = 10, side = 1, method = "CS")
negbintol.int(x = 50, n = 10, side = 1, method = "SC")
negbintol.int(x = 50, n = 10, side = 1, method = "LR")
negbintol.int(x = 50, n = 10, side = 1, method = "SP")
negbintol.int(x = 50, n = 10, side = 1, method = "CC")
## 95%/99% 1-sided tolerance limits and 2-sided tolerance
## interval for the same setting above, but when we are
## interested in a future experiment that requires 20 successes
## be reached for each trial.
negbintol.int(x = 50, n = 10, m = 20, side = 1)
negbintol.int(x = 50, n = 10, m = 20, side = 2)
``` |

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