Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne


  • Bruce E. TrumboEmail author
  • Eric A. Suess
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_110189


 In probability modeling: Monte Carlo procedures, Random sampling with pseudo-random numbers.  In statistical inference: Bootstraps, (simulated) permutation tests, Markov chain Monte Carlo (MCMC)


Beta distributions

The general density function is \( f\left(x,\mid, \alpha,, \beta \right)=\frac{\varGamma \left(\alpha +\beta \right)}{\varGamma \left(\alpha \right)\varGamma \left(\beta \right)}{x}^{\alpha -1}{\left(1-x\right)}^{\beta -1},\,\, \)

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Several of the examples and figures here are adapted from material in the first three chapters of Suess and Trumbo (2010) and in Trumbo (2006). Our perspectives on simulation have been influenced by Braun and Murdoch (2007), Blitzstein and Hwang (2015), Grolemund and Wickham (2014), Gentle (1998), and Venables and Ripley (2002). We thank colleagues, current and former students, three anonymous referees, and our associate editor for useful suggestions.

The simulations in this article used R statistical software (open-source software available without cost from www.r-project.org for use on Windows, Macintosh, or UNIX operating systems). We hope our descriptions and examples of code are sufficiently clear that readers could repeat our simulations using other software. Python open-source software may be the most convenient alternative. Commercial software such as Mathematica, SAS, and Excel can also do simulations, but they may lack analogues of the specialized functions for probability and statistics we have used.


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© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and BiostatisticsCalifornia State University, East BayHaywardUSA

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates