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Minitab estimates the shape and scale using one of three estimation methods: maximum likelihood, conditional maximum likelihood, and least squares.

The log-likelihood is a measure of the fit of the distribution. When estimating the shape and scale parameters, Minitab will make this number as large as possible. By maximizing the likelihood function, Minitab calculates the maximum likelihood and conditional maximum likelihood estimates.

Minitab displays output in the Session window based on the chosen estimation method and whether or not the shape parameter is known. The differences are shown in the table below:

Method |
Shape |
Parameter estimates |
Standard error and confidence intervals |

Maximum likelihood |
Unknown |
Shape and scale |
Yes |

Maximum likelihood |
Known, = 1 |
Yes | |

Maximum likelihood |
Known, not 1 |
Scale |
Yes |

Conditional maximum likelihood |
Unknown |
Shape and scale |
For shape only |

Least squares |
Unknown |
Shape and scale |
No |

Least squares |
Known, = 1 |
MTBF |
No |

Least squares |
Known, not 1 |
Scale |
No |

See Comparison of growth curve procedures for a discussion of the advantages and disadvantages of each method.