NDLI: Chord-length distribution functions and Rice formulae. Application to random media

Content Provider	Springer Nature Link
Author	Estrade, Anne Iribarren, Ileana Kratz, Marie
Copyright Year	2011
Abstract	We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it, and see each line as a one-dimensional level-cut process with value 0 or 1 according to whether a regular stationary process X is less or greater than a given level. The intervals corresponding to the points at which X is in a given phase are named chords. We are interested in obtaining information on the chord-length distribution functions. Working with the Palm probability measure and using level crossings techniques, in particular Rice methods, we can obtain not only the exact analytical formula of the chord-length distribution function but also the joint distribution function of the lengths of two successive chords. Finally, we indicate some concrete applications for the computation of usual stereological parameters.
Starting Page	333
Ending Page	352
Page Count	20
File Format	PDF
ISSN	13861999
Journal	Extremes
Volume Number	15
Issue Number	3
e-ISSN	1572915X
Language	English
Publisher	Springer US
Publisher Date	2011-07-28
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chord (Up/down) crossing Gaussian process Level-cut process Palm probability Porous medium Rice formula Environmental Management Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Hydrogeology Civil Engineering Quality Control, Reliability, Safety and Risk
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics, Econometrics and Finance Engineering

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