# On particle-size distribution of convex similar bodies in $\mathbb{R}^3$

@article{Kisevlak2019OnPD, title={On particle-size distribution of convex similar bodies in \$\mathbb\{R\}^3\$}, author={Jozef Kisevl'ak and Gabriela Bal'uchov'a}, journal={arXiv: Probability}, year={2019} }

We give an explicit form of particle-size distributions of convex similar bodies for random plane and random line, which naturally generalize famous Wicksell's corpuscle problem. The results are achieved by applying the Method of Model Solutions for solving well-known Santalo's integral equations. We also give a partial result related to the question of existence and uniqueness of these solutions. We finally illustrate our approach on several examples.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 11 REFERENCES

## Integral geometry and geometric probability

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## THE CORPUSCLE PROBLEM. A MATHEMATICAL STUDY OF A BIOMETRIC PROBLEM

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Stereology for Statisticians

VIEW 1 EXCERPT

## A direct approach to the mellin transform

VIEW 1 EXCERPT

## Mellin Transforms and Asymptotics: Harmonic Sums

VIEW 1 EXCERPT

## INTEGRAL GEOMETRY IN Rn

VIEW 2 EXCERPTS

## Abel Integral Equations: Analysis and Applications

VIEW 1 EXCERPT