Comments on: Everything you wanted to know about power-laws but were afraid to ask http://groundtruth.info/AstroStat/slog/2007/astroph-07061062/ Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 12 Aug 2011 17:44:19 +0000 http://wordpress.org/?v=2.9 hourly 1 By: hlee http://groundtruth.info/AstroStat/slog/2007/astroph-07061062/comment-page-1/#comment-183 hlee Tue, 08 Apr 2008 07:52:51 +0000 http://groundtruth.info/AstroStat/slog/2007/astroph-07061062/#comment-183 I completely forgot to comment on this post but my recent post on <a href="http://groundtruth.info/AstroStat/slog/2008/arxiv-pareto-distribution/" rel="nofollow">the Pareto distribution</a> brought me back. Though it may not be a complete answer, I wanted to say that I learned applying the K-S test for the first time to test a homogeneous Poisson process from a spatial statistics class in a similar manner as this paper describes. Trials of 99 times of simulations allow to rank the K-S test stat from the data to determine a p-value. Instead of 99 times, for the accuracy, the paper suggests 2500 synthetic data sets. I'd like to second you that this is a very handy reference, particularly it may resolve concerns on the non-nested hypothesis testing (<a href="http://groundtruth.info/AstroStat/slog/2008/non-nested-hypothesis-tests/" rel="nofollow">the slog post</a> has the same reference, Vuong (1989) and other relevant ones) in astronomy. I dare to quote a line from their conclusion: <i>The common practice of identifying and quantifying power-law distributions by the approximately straight-line behavior of a histogram on a doubly logarithmic plot is known to give biased results and should not be trusted.</i> Appendix has its explanation and gives a second thought when fitting a straight line or even two straight lines connected at a breaking point (broken power laws). I completely forgot to comment on this post but my recent post on the Pareto distribution brought me back. Though it may not be a complete answer, I wanted to say that I learned applying the K-S test for the first time to test a homogeneous Poisson process from a spatial statistics class in a similar manner as this paper describes. Trials of 99 times of simulations allow to rank the K-S test stat from the data to determine a p-value. Instead of 99 times, for the accuracy, the paper suggests 2500 synthetic data sets.

I’d like to second you that this is a very handy reference, particularly it may resolve concerns on the non-nested hypothesis testing (the slog post has the same reference, Vuong (1989) and other relevant ones) in astronomy.

I dare to quote a line from their conclusion: The common practice of identifying and quantifying power-law distributions by the approximately straight-line behavior of a histogram on a doubly logarithmic plot is known to give biased results and should not be trusted. Appendix has its explanation and gives a second thought when fitting a straight line or even two straight lines connected at a breaking point (broken power laws).

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