Description Usage Arguments Details Value References See Also Examples

Provides 1-sided or 2-sided tolerance intervals for data distributed according to either a Pareto distribution or a power distribution (i.e., the inverse Pareto distribution).

1 2 | ```
paretotol.int(x, alpha = 0.05, P = 0.99, side = 1,
method = c("GPU", "DUN"), power.dist = FALSE)
``` |

`x` |
A vector of data which is distributed according to either a Pareto distribution or a power distribution. |

`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 how the upper tolerance bound is approximated when transforming to utilize the relationship with the 2-parameter
exponential distribution. |

`power.dist` |
If |

Recall that if the random variable *X* is distributed
according to a Pareto distribution, then the random variable *Y
= ln(X)* is distributed according to a 2-parameter exponential
distribution. Moreover, if the random variable *W* is
distributed according to a power distribution, then the random
variable *X = 1/W* is distributed according to a Pareto
distribution, which in turn means that the random variable *Y =
ln(1/W)* is distributed according to a 2-parameter exponential
distribution.

`paretotol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

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

`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 |

Dunsmore, I. R. (1978), Some Approximations for Tolerance Factors for the Two Parameter Exponential Distribution,
*Technometrics*, **20**, 317–318.

Engelhardt, M. and Bain, L. J. (1978), Tolerance Limits and Confidence Limits on Reliability for the Two-Parameter
Exponential Distribution, *Technometrics*, **20**, 37–39.

Guenther, W. C., Patil, S. A., and Uppuluri, V. R. R. (1976), One-Sided *β*-Content Tolerance Factors
for the Two Parameter Exponential Distribution, *Technometrics*, **18**, 333–340.

Krishnamoorthy, K., Mathew, T., and Mukherjee, S. (2008), Normal-Based Methods for a Gamma Distribution:
Prediction and Tolerance Intervals and Stress-Strength Reliability, *Technometrics*, **50**, 69–78.

`TwoParExponential`

, `exp2tol.int`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## 95%/99% 2-sided Pareto tolerance intervals
## for a sample of size 500.
set.seed(100)
x <- exp(r2exp(500, rate = 0.15, shift = 2))
out <- paretotol.int(x = x, alpha = 0.05, P = 0.99, side = 2,
method = "DUN", power.dist = FALSE)
out
plottol(out, x, plot.type = "both", side = "two",
x.lab = "Pareto Data")
``` |

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