AVar (MLE) is the asymptotic variance and ACov (,) is the asymptotic covariance of the MLEs of μ, σ, θ, and β taken from the appropriate element of the inverse of the Fisher information matrix. For more information, see Meeker and Escobar^{1}.

The sample size needed to estimate the percentile, t_{p}, is calculated as follows:

- For a two-sided confidence interval
- For a one-sided confidence interval

Term | Description |
---|---|

N | sample size |

t_{p,mle} | ML estimate of t_{p} |

D_{T} | distance between the estimate and the upper (or lower) bound of the (1 – α)100% confidence interval |

Φ^{-1 } | inverse CDF of the chosen model |

Φ^{-1 }nor | inverse CDF of the normal distribution |

- For a two-sided confidence interval
- For a one-sided confidence interval

Term | Description |
---|---|

N | sample size |

t_{p,mle} | ML estimate of t_{p} |

R_{T} | precision when the upper (or lower) bound of the (1 – α)100% confidence interval falls X percent away from the MLE. For an upper bound, R_{T} =1 + X/100. For a lower bound, R_{T} = 1/(1-X/100). |

Φ^{-1 } | inverse CDF for the chosen model |

Φ^{-1 }nor | inverse CDF of the normal distribution |

- For a two-sided confidence interval
- For a one-sided confidence interval

where

for the lower bound

for the upper bound

for normal, logistic, and smallest extreme value distributions

for Weibull, lognormal, and loglogistic distributions

Term | Description |
---|---|

N | sample size |

μ_{mle} | MLE estimate of mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

σ_{mle} | MLE estimate of scale parameter |

D_{T} | precision |

Φ^{-1 } | inverse CDF of the chosen model |

Φ^{-1 }nor | inverse CDF of the normal distribution |