Description Usage Arguments Value Note References See Also Examples

Provides 1-sided or 2-sided tolerance intervals for negative hypergeometric random variables. When sampling without replacement, these limits are on the total number of expected draws in a future sample in order to achieve a certain number from group A (e.g., "black balls" in an urn).

1 2 | ```
neghypertol.int(x, n, N, m = NULL, alpha = 0.05, P = 0.99,
side = 1, method = c("EX", "LS", "CC"))
``` |

`x` |
The number of units drawn in order to achieve |

`n` |
The target number of successes in the sample drawn (e.g., the number of "black balls" you are to draw in the sample). |

`N` |
The population size (e.g., the total number of balls in the urn). |

`m` |
The target number of successes to be sampled from the universe for a future study. If |

`alpha` |
The level chosen such that |

`P` |
The proportion of units from group A 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 |

`neghypertol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

`P` |
The proportion of units from group A in future samples of size |

`rate` |
The sampling rate determined by |

`p.hat` |
The proportion of units in the sample from group A, 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 |

As this methodology is built using large-sample theory, if the sampling rate is less than 0.05, then a warning is generated stating that the results are not reliable.

Khan, R. A. (1994), A Note on the Generating Function of a Negative Hypergeometric Distribution,
*Sankhya: The Indian Journal of Statistics, Series B*, **56**, 309–313.

Young, D. S. (2014), Tolerance Intervals for Hypergeometric and Negative Hypergeometric Variables,
*Sankhya: The Indian Journal of Statistics, Series B*, **77**(1), 114–140.

1 2 3 4 5 6 7 8 | ```
## 90%/95% 2-sided negative hypergeometric tolerance
## intervals for a future number of 20 successes when
## the universe is of size 100. The estimates are
## based on having drawn 50 in another sample to achieve
## 20 successes.
neghypertol.int(50, 20, 100, m = 20, alpha = 0.05,
P = 0.95, side = 2, method = "LS")
``` |

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