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 new 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. We calculate the asymptotic relative efficiency of the estimators and show that the new estimator based on the rectangles is more efficient. We obtain also the confidence intervals for π. The data of a real experiment is provided.
Fazli, K. & Erzideh, C. (2022). Statistical estimation of the number π by rectangles in Buffon’s needle problem
continuing title in this line (if required). Andishe_ye Amari, 26(2), 67-71.
MLA
Fazli, K., & Erzideh, C. "Statistical estimation of the number π by rectangles in Buffon’s needle problem
continuing title in this line (if required)", Andishe_ye Amari, 26, 2, 2022, 67-71.
HARVARD
Fazli K., Erzideh C. (2022). 'Statistical estimation of the number π by rectangles in Buffon’s needle problem
continuing title in this line (if required)', Andishe_ye Amari, 26(2), pp. 67-71.
CHICAGO
K. Fazli & C. Erzideh, "Statistical estimation of the number π by rectangles in Buffon’s needle problem
continuing title in this line (if required)," Andishe_ye Amari, 26 2 (2022): 67-71,
VANCOUVER
Fazli K., Erzideh C. Statistical estimation of the number π by rectangles in Buffon’s needle problem
continuing title in this line (if required). Andishe_ye Amari. 2022;26(2):67-71 (In Persian).
