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Length Bias in the Measurements of Carbon Nanotubes

Summary: [This abstract is based on the author’s abstract.] Current methods of measuring carbon nanotubes on a square grid do not include nanotubes that cross the grid, resulting in samples that are length-biased. A nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of length-bias are examined. The corrected length distribution estimate provides a better fit to the Weibull distribution than the original selection-based observations, reinforcing a previous claim about the underlying distribution of synthesized nanotube lengths.

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  • Topics: Design of Experiments
  • Keywords: Censored data, Goodness of fit, Nonparametric methods, Probability, Sampling, Selection, Weibull distribution,
  • Author: Kvam, Paul
  • Journal: Technometrics