Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I would like to ask you where you spot the mistake in the derivatives of the loglikelihood function of the cauchy distribution, as I am breaking my head :( I apply this to a newton optimization procedure and got correct m, but wrong scale parameter s. Thanks!

[tex]

LLF = -n\ln(pi)+n\ln(s)-\sum(\ln(s^2+(x-m)^2)),

[/tex]

First Derivatives:

[tex]

\frac {dL} {dm} = 2\sum(x-m) / \sum(s^2+(x-m)^2)

[/tex]

[tex]

\frac {dL} {ds} = n/s - 2\sum(s) / \sum(s^2+(x-m)^2)

[/tex]

Second Derivatives:

[tex]

\frac {d^2L} {dm^2} = (-2n(\sum(s^2+(x-m)^2)))+4\sum(x-m)^2)/(\sum(s^2+(x-m)^2))^2

[/tex]

[tex]

\frac {d^2L} {ds^2} =-n/s^2-2\sum(-s^2+(x-m)^2)/(\sum(s^2+(x-m)^2))^2

[/tex]

[tex]

\frac {d^2L} {dmds} =-4\sum(s(x-m))/(\sum(s^2+(x-m)^2))^2

[/tex]

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivatives of Cauchy Distribution

Loading...

Similar Threads - Derivatives Cauchy Distribution | Date |
---|---|

I Derivative and Parameterisation of a Contour Integral | Feb 7, 2018 |

I Why does this concavity function not work for this polar fun | Jan 26, 2018 |

I Euler Lagrange formula with higher derivatives | Jan 24, 2018 |

I Derivative of infinitesimal value | Jan 15, 2018 |

Reading Cauchy's lecture on the derivative | Apr 5, 2013 |

**Physics Forums - The Fusion of Science and Community**