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On the distribution and moments of the strength of a bundle of filaments

Published online by Cambridge University Press:  14 July 2016

M. W. Suh ,
B. B. Bhattacharyya  and
A. Grandage
M. W. Suh
Affiliation:
Burlington Industries Inc., Greensboro, N. C.
B. B. Bhattacharyya
Affiliation:
North Carolina State University
A. Grandage
Affiliation:
North Carolina State University
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Summary

Small sample and large sample properties of the bundle strength of parallel filaments studied earlier by Daniels (1945) and Sen, Bhattacharyya, Suh (1969) have been developed here by probabilistic argument. The statistics belong to a family or class of statistics, each of which forms a reverse semi-martingale sequence. Certain moment properties are also discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 712 - 720
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads. Proc. Roy. Soc. A 183, 405–435.Google Scholar
[2] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
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[4] Schmid, P. (1958) On the Kolomogorov and Smirnov limit theorems for discontinuous distribution functions. Ann. Math. Statist. 29, 1011–1027.CrossRefGoogle Scholar
[5] Sen, P. K., Bhattacharyya, B. B. and Suh, M. W. (1969) Limiting behaviour of the extremum of certain sample functions. Mimeo Series No. 628. Institute of Statistics. Consolidated University of North Carolina. (Submitted for publication.).Google Scholar
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