Description Usage Arguments Value References See Also Examples

Provides 1-sided or 2-sided tolerance intervals for Poisson random variables. From a statistical quality control perspective, these limits bound the number of occurrences (which follow a Poisson distribution) in a specified future time period.

1 2 3 | ```
poistol.int(x, n, m = NULL, alpha = 0.05, P = 0.99, side = 1,
method = c("TAB", "LS", "SC", "CC", "VS", "RVS",
"FT", "CSC"))
``` |

`x` |
The number of occurrences of the event in time period |

`n` |
The time period of the original measurements. |

`m` |
The specified future length of time. If |

`alpha` |
The level chosen such that |

`P` |
The proportion of occurrences in future time lengths 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 |

`poistol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

`P` |
The proportion of occurrences in future time periods of length |

`lambda.hat` |
The mean occurrence rate per unit time, 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 |

Barker, L. (2002), A Comparison of Nine Confidence Intervals for a Poisson Parameter When the Expected Number of Events Is *≤ 5*, *The American Statistician*, **56**, 85–89.

Freeman, M. F. and Tukey, J. W. (1950), Transformations Related to the Angular and the Square Root,
*Annals of Mathematical Statistics*, **21**, 607–611.

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | ```
## 95%/90% 1-sided Poisson tolerance limits for future
## occurrences in a period of length 3. All seven methods
## are presented for comparison.
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "TAB")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "LS")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "SC")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "CC")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "VS")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "RVS")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "FT")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "CSC")
## 95%/90% 2-sided Poisson tolerance intervals for future
## occurrences in a period of length 15. All seven methods
## are presented for comparison.
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "TAB")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "LS")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "SC")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "CC")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "VS")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "RVS")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "FT")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
side = 2, method = "CSC")
``` |

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