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Biometrika 1972 59(2):415-426; doi:10.1093/biomet/59.2.415
© 1972 by Biometrika Trust
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Sampling procedures for the lengths of random straight lines

RODNEY COLEMAN

Imperial College London

A process of random straight lines of finite length is defined, and tests are constructed for its validity. Methods of sampling for the length distribution of lines from the process are summarized and criticized. The search and measure procedures in particular are analyzed in detail. Under these procedures a fixed point is chosen independently of the process of lines; the line having an end closest to the fixed point is measured; and the other end of that line is then used as the next fixed point for further sampling. Recommendations are made by which these procedures can be modified to yield a random sample of lengths from the process.

Key Words: Nuclear particle tracks • Line and cluster processes • Rank tests for directions • Unbiased and length-biased sampling • Search and measure sampling • Geometrical probability


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