The procedure of finding the value of one or more parameters for a given statistic which makes the *known*
Likelihood distribution a Maximum. The maximum likelihood estimate for a parameter is denoted
.

For a Bernoulli Distribution,

(1) |

(2) |

where or 1, and , ..., .

(3) |

(4) |

(5) |

(6) |

For a Gaussian Distribution,

(7) |

(8) |

(9) |

(10) |

(11) |

(12) |

For a weighted Gaussian Distribution,

(13) |

(14) |

(15) |

(16) |

(17) |

(18) |

(19) |

For a Poisson Distribution,

(20) |

(21) |

(22) |

(23) |

**References**

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Least Squares as a Maximum Likelihood
Estimator.'' §15.1 in
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England:
Cambridge University Press, pp. 651-655, 1992.

© 1996-9

1999-05-26