Analysis of Heavy Tailed Distributions

An implementation of maximum likelihood estimators for a variety of heavy tailed distributions, including both the discrete and continuous power law distributions. Additionally, a goodness-of-fit based approach is used to estimate the lower cut-off for the scaling region.


Version 0.70.1

  • Bug fix: Very rarely bootstrapping results in singular datasets.

Version 0.70.0

  • Update documentation
  • Bug fix: 1 sided p-value for Vuong's.
  • Now pass a matrix of parameters when estimating xmin (fixes #68). Used for lognormal distribution.

Version 0.60.3

  • Incorrect p-value for bootstrap_p (fixes #64). Thanks to @lsaravia for reporting.

Version 0.60.0

Version 0.50.1 (not on CRAN)

Version 0.50.0

  • Added get_ntail function which returns the number of points greater than or equal to xmin.
  • Added get_n function which returns the sample size.
  • Bug fix: bootstrap_p was incorrect for CTN models ( Thanks to @lsaravia for reporting and diagnosing the problem.

Version 0.40.0 (not on CRAN)

  • Add ByteCompile flag. Testing suggests that bootstrapping is now around twice as fast.
  • Added seed and package_version to the output of bootstrap and bootstrap_p.
  • Added poisson random number generator.

Version 0.30.2

  • Bug fix: Plotting the data cdf failed when data values were larger than xmax ( Thanks to @LaurentFranckx

Version 0.30.1

  • Bug fix: pdf and cdf functions should now handle values of q less than xmin in a sensible way (Thanks to Pierce Brookss)

Version 0.30.0

  • New package title to satisfy CRAN
  • A new xmax argument has been added to the bootstrap and estimate_xmin functions. This argument limits the search space when calculating the KS statistic.
  • The all_values argument has been removed from dist_cdf. A new function dist_all_cdf has been created.
  • Added random number generators for log normal and exponential functions (
  • Added seed argument to bootstrap and bootstrap_p functions
  • Added warning message to handle estimation in tail regions (
  • Bug fix: Bootstrap edge cases ( @jkeirstead

Version 0.20.5

  • Further changes to the tolerance in the test suite comparison (Solaris-sparc failed to build)

Version 0.20.4

  • Added tolerance to test suite comparison (Solaris-sparc failed to build)
  • Removed tufte vignette styles

Version 0.20.3

  • Test suite now included in the package
  • Improved numerical stability when working out discrete exp and log normal pdfs (
  • Merged data_max and xmins argument in estimate_xmin function
  • Added example on copying distribution objects (
  • Added new vignette on comparing distributions (
  • Bug fix: When estimating xmin is not possible (e.g. not enough data), estimate_xmin now returns NA rather than an error (
  • Bug fix: When setting parameters in distributions, no longer a strict class comparison
  • Bug fix: Error when the length of xmins is 1 in estimate_xmin ( Thanks to @linzhp
  • Bug fix: Generating random numbers for the discrete power-law distribution wasn't quite right for small x values. ( Thanks to @wrhaas.

Version 0.20.2

  • Discrete power-law mle now uses L-BFGS-B optimiser by default
  • Vignette source now included within the package
  • Bug fix in lines methods
  • Bug fix: use data_max argument in estimate_xmin ( Thanks to @pgoldberg.

Version 0.20.1

  • Updated documentation
  • Added swiss_prot data set
  • Renamed NativeAmerican to native_american
  • Renamed USAmerican to us_american
  • Changed license to GPL-2 | GPL-3

Version 0.20.0

  • Added discrete exponential function
  • Added compare_distribution functions
  • dist_pdf now have a log argument
  • Updated documentation
  • Bug fixes

Version 0.17.0

  • Added discrete log normal, log normal and poisson distributions.
  • Generic plot functions added for bootstrap output.
  • Test suite.
  • New examples vignette.
  • Bug fixes

Version 0.16.1

  • bootstrap_xmin now implements the procedure described in Clauset
  • bootstrap_p estimates the p-value

Version 0.16.0

  • Added dist_data_cdf_function
  • Can now plot the entire data line and add distribution lines starting at xmin
  • Added vignette
  • Improved documentation
  • Deprecated pl_data data class

Version 0.15.2

  • Generating discrete random numbers took up too much memory. Reduced the threshold for switching to the CTN PL distribution.

Version 0.15.1

  • Bug fix in the lines and points function

Version 0.15.0

  • Adding support for continuous power-laws

Version 0.14.4

  • No visible changes - preparing for future R versions.
  • Added discrete_xmax parameter to the discrete random number generator. This parameter controls where we change from using a (true) discrete random number generator to a CTN approximation.

Version 0.14.3

  • xmin now set to minimum value of x

Version 0.14.2

  • Plots, lines and points functions now return the data using invisible
  • Moved to parSapplyLB
  • Added a bootstrap_moby data set.

Version 0.14.1

  • Bug fix when calculating the bootstrapping p-value

Version 0.14

  • Added explicit garbage collection call to the bootstrap routine to avoid memory issues.

Version 0.13

  • Created the estimate_pars method - an mle estimate of the parameters.

Version 0.12

  • Fixed bug when calculating the KS statistics
  • Updated docs

Version 0.11

  • Fixed bug in random number generator
  • Updated docs

Version 0.1

  • Initial release

Reference manual

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0.70.2 by Colin Gillespie, 12 days ago

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Browse source code at

Authors: Colin Gillespie [aut, cre]

Documentation:   PDF Manual  

Task views: Probability Distributions

GPL-2 | GPL-3 license

Imports VGAM, parallel, methods, utils, stats

Suggests knitr, R.matlab, testthat, codetools, covr

Imported by BTR, SNscan, randnet.

Depended on by AbSim.

Suggested by ercv, poppr, spatialwarnings.

See at CRAN