Select the method or formula of your choice.

The probability plots include:

- Points, which are the estimated percentiles for corresponding probabilities of an ordered data set.
- Middle lines, which are the expected percentile from the distribution based on maximum likelihood parameter estimates. If the distribution is a good fit for the data, the points fall along the middle line.

Minitab estimates the probability (P) that is used to calculate the plot points using the following methods.

- Median rank (Benard's method)
- Mean Rank (Herd-Johnson estimate)
- Modified Kaplan-Meier (Hazen)
- Kaplan-Meier product limit estimate

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

n | Number of observations |

i | Rank of the i^{th} ordered observation x(i), where x(1), x(2),...x(n) are the order statistics, or the data ordered from smallest to largest |

The middle line of the probability plot is constructed using the x and y coordinate calculations in this table.

Distribution | x coordinate | y coordinate |
---|---|---|

Smallest extreme value | x | ln(–ln(1 – p)) |

Largest extreme value | x | ln(–ln p) |

Weibull | ln(x) | ln(–ln(1 – p)) |

Exponential | ln(x) | ln(–ln(1 – p)) |

Lognormal | ln(x) | Φ^{–1}_{norm} |

Logistic | x | |

Loglogistic | ln(x) | |

Gamma | x | Φ^{–1}_{gamma} |

Because the plot points do not depend on any distribution, they are the same (before being transformed) for any probability plot. However, the fitted line differs depending on the parametric distribution chosen.

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

p | The estimated probability |

Φ-^{1}_{norm} | Value returned for p by the inverse CDF for the standard normal distribution |

Φ-^{1}_{gamma} | Value returned for p by the inverse CDF for the incomplete gamma distribution |

ln(x) | The natural log of x |