### Abstract

The power law arises commonly in modeling the number of vertices of a given degree in large graphs. In estimating the degree of the power law, the typical approach is to truncate by eye the log-log plot, then fit a linear equation to the remaining log-transformed data. Here we formulate a hard-coded truncation rule to replace the visual truncation, justify it by showing that the truncation point goes to infinity and misses a vanishing fraction of the data with probability tending to one, and refine the subsequent regression with a weighting and a way to use the covariation between slope and intercept to optimize the slope estimate.

Original language | English (US) |
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Pages (from-to) | 19-28 |

Number of pages | 10 |

Journal | Internet Mathematics |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2009 |

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics

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## Cite this

Abramson, I., & Berg, A. (2009). An occupancy problem arising in power law fitting.

*Internet Mathematics*,*6*(1), 19-28. https://doi.org/10.1080/15427951.2009.10129178