Simulate and Visualize Kendall Random Walks and Related Distributions

Kendall random walks are a continuous-space Markov chains generated by the Kendall generalized convolution. This package provides tools for simulating these random walks and studying distributions related to them. For more information about Kendall random walks see Jasiulis-Gołdyn (2014) .

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Simulations and distributions related to Kendall random walks: visit dedicated project page on Researchgate

To get started, install stable CRAN version

or the newest version from Github:




Main functionalities:

  • simulate_kendall_rw functions simulates Kendall random walks for a given step distribution. The simulation can be then plotted using generic plot function.
  • transform_kendall_rw function allows user to play with different scalings and transformations of Kendall random walks to study its properties related to convergence.
  • summarise_kendall_rw and mutate_kendall_rw functions allow user to modify or summarise simulated trajectories.
  • ladder_moment and ladder_height functions help study distribution of first ladder moment and first ladder height empirically.
  • ladder_moment_pmf gives exact PMF for first ladder moment.
  • pkend, dkend, qkend and rkend are typical functions related to the stable Kendall distribution.
  • g_function calculates Williamson transform numerically.

See vignettes for examples.

If you have a feature request or you found a bug, please leave an issue.

The goal of this package is to let anyone interested in Kendall convolution/generalized convolutions get familiar with them through visual means and experimentation and aid research in this area by providing tools for simulations.


This work is a part of project "First order Kendall maximal autoregressive processes and their applications", which is carried out within the POWROTY/REINTEGRATION programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.


kendallRandomWalks 0.9.4

  • Print and plot methods for the result of summarise_kendall_rw function.
  • Finished vignettes.

kendallRandomWalks 0.9.3

  • EnvStats dependency replaced by actuar.

kendallRandomWalks 0.9.2

  • Functions for transformations and summaries of simulations of Kendall random walks (summarise_kendall_rw and mutate_kendall_rw).
  • Name changed to kendallRandomWalks

kendallRandomPackage 0.9.1

  • Numerical computation of G function (so also Williamson transform)
  • Exact distribution of first ladder moments

kendallRandomPackage 0.9.0

  • Generic function for printing and plotting simulation objects
  • Barrier crossing simulations and visualizations


  • Added a file to track changes to the package.

Reference manual

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0.9.4 by Mateusz Staniak, 3 years ago

Browse source code at

Authors: Mateusz Staniak [aut, cre]

Documentation:   PDF Manual  

MIT + file LICENSE license

Imports ggplot2, dplyr, tibble, actuar

Suggests knitr, rmarkdown, testthat, covr

See at CRAN