Orientation-dependent distribution of the length of a random segment and covariogram

The paper considers a random segment L with fixed direction and length that intersects a given bounded convex body D in the n-dimmensional Euclidean space. We obtain a relationship between the covariogram of D and the distribution of the random variable the length of L. A relationship between the distribution of the length of L and the orientation-dependent chord length distribution is also obtained. As a consequence, we obtain a relationship between the chord length distribution function and the distribution of the random variable length of L.

Ara Gasparyan, Victor Ohanyan

Journal of Contemporary Mathematical Analysis 50 (2), 90–97, 2015

Covariogram, distribution of the length of a random segment, convex body

60D05, 52A22, 53C65

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