Understanding convergence concepts: a visual-minded and graphical simulation-based approach

Pierre Lafaye De Micheaux; Benoit Liquet

doi:10.1198/tas.2009.0032

Understanding convergence concepts: a visual-minded and graphical simulation-based approach

Pierre Lafaye De Micheaux, Benoit Liquet

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This article describes the difficult concepts of convergence in probability, convergence almost surely, convergence in law, and convergence in rth mean using a visual-minded and graphical simulation-based approach. For this purpose, each probability of events is approximated by a frequency. An R package that reproduces all of the experiments cited in this article is available in CRAN. See the online Supplement for details.

Original language	English
Pages (from-to)	173-178
Number of pages	6
Journal	American Statistician
Volume	63
Issue number	2
DOIs	https://doi.org/10.1198/tas.2009.0032
Publication status	Published - 2009
Externally published	Yes

Keywords

Convergence almost surely
Convergence in law
Convergence in probability
Convergence in rth mean
Dynamic graphics
Monte carlo simulation
R language
Visualization

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10.1198/tas.2009.0032

Cite this

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AB - This article describes the difficult concepts of convergence in probability, convergence almost surely, convergence in law, and convergence in rth mean using a visual-minded and graphical simulation-based approach. For this purpose, each probability of events is approximated by a frequency. An R package that reproduces all of the experiments cited in this article is available in CRAN. See the online Supplement for details.

KW - Convergence almost surely

KW - Convergence in law

KW - Convergence in probability

KW - Convergence in rth mean

KW - Dynamic graphics

KW - Monte carlo simulation

KW - R language

KW - Visualization

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Understanding convergence concepts: a visual-minded and graphical simulation-based approach

Abstract

Keywords

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