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Statistical estimation of the number π by rectangles in Buffon’s needle problem
Khosrow Fazli *, Korosh Arzideh
University of Kurdistan
Abstract:   (211 Views)
The Buffon’s needle problem is a random experiment leading to estimate of the number π by ”randomly” throwing a
needle onto a plane partitioned by parallel lines. Indeed, in the independently repetitions of the experiment, based on
the number of times where the needle will cross a line, one can construct an estimator of π. The aim of this note is to
obtain a better estimator (in some sense) by considering a model where the plane is partitioned by rectangles. We show
that both estimators are asymptotically normal and unbiased; and also the confidence intervals are obtained for π. We
calculate the asymptotic relative efficiency of the estimators and show that the estimator based on the rectangles is more
efficient. The data of a real experiment is provided.
Keywords: Asymptotic relative efficiency, asymptotically normal, asymptotically unbiased
Full-Text [PDF 185 kb]   (243 Downloads)    
Type of Study: case report | Subject: General
Received: 2021/05/23 | Accepted: 2022/03/30
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