The AstroStat Slog » survival function http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 [ArXiv] Pareto Distribution http://hea-www.harvard.edu/AstroStat/slog/2008/arxiv-pareto-distribution/ http://hea-www.harvard.edu/AstroStat/slog/2008/arxiv-pareto-distribution/#comments Thu, 03 Apr 2008 20:55:04 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/?p=265 Astronomy is ruled by Gaussian distribution with a Poisson distribution duchy. From time to time, ranks are awarded to other distributions without their own territories to be governed independently. Among these distributions, Pareto deserves a high rank. There is a preprint of this week on the Pareto distribution:

    On the Truncated Pareto Distribution with applications by Zaninetti and Ferraro [astro-ph:0804.0308]
    
From the abstract:

This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of mass of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented.

The paper introduces the pdf, cdf, mean, variance, higher moments, and survival function of the (truncated) Pareto distribution with applications to Star masses from the Hipparcos data[1] and asteroid sizes, and simulations of primeval nebula[2]. It concludes that the truncated Pareto works better than the usual Pareto. The Pareto distribution is simple and intuitive.

ps. Not many astronomy papers cite papers from recent statistical publications. I witness that although the most of astronomical papers have no needs for citing papers in statistics, if they do, they tend to have references from four to five decades ago among which books were revised in 90′s or later and articles of modern perspectives are available (exceptions are seminal papers that introduced statistics to the community like EM algorithm). It is quite encouraging to see an article from JASA 2006 was cited in [astro-ph:0804.0308]

  1. Pareto or power law seems not a good model to fit star masses
  2. Mass accretion observes probabilistic model, I guess
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