DOI
10.1198/004017008000000442
Abstract
To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length distribution estimate provides a better fit to the Weibull distribution than the original selection-biased observations, thus reinforcing a previous claim about the underlying distribution of synthesized nanotube lengths.
Document Type
Post-print Article
Publication Date
2008
Publisher Statement
Copyright © 2008 Taylor & Francis.
DOI: 10.1198/004017008000000442
The definitive version is available at: https://amstat.tandfonline.com/doi/abs/10.1198/004017008000000442#.WxBuNEgvyCp
Full Citation:
Kvam, Paul H. "Length Bias in the Measurements of Carbon Nanotubes." Technometrics 50, no. 4 (2008): 462-467. doi:10.1198/004017008000000442.
Recommended Citation
Kvam, Paul H., "Length Bias in the Measurements of Carbon Nanotubes" (2008). Department of Math & Statistics Faculty Publications. 207.
https://scholarship.richmond.edu/mathcs-faculty-publications/207