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Throwing Buffon's Needle with Mathematica
Enis Siniksaran

It has long been known that Buffon's needle experiments can be used to estimate Pi. Three main factors influence these experiments: grid shape, grid density, and needle length. In statistical literature, several experiments depending on these factors have been designed to increase the efficiency of the estimators of Pi and to use all the information as fully as possible. We wrote the package BuffonNeedle to carry out the most common forms of Buffon's needle experiments. In this article we review statistical aspects of the experiments, introduce the package BuffonNeedle, discuss the crossing probabilities and asymptotic variances of the estimators, and describe how to calculate them using Mathematica.

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About the Author
Enis Siniksaran is an assistant professor at Istanbul University, Department of Econometrics. His research interests include geometric approaches to statistical methods, robust statistical methods, and the methodology of econometrics. He has been working with Mathematica since 1998. For details on his recent work dealing with the geometry of classical test statistics, in which all symbolic and numerical computations and graphical work are done using Mathematica, see library.wolfram.com/infocenter/Articles/5962.

Enis Siniksaran
Istanbul Universitesi, Iktisat Fak., Ekonometri Bolumu Beyazıt, 34452, Istanbul, Turkey
saran@istanbul.edu.tr


     
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