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random tesselation; stereology; lens-shaped discs; stereological model; parameter estimations

References:

[1] R. Coleman: **An Introduction to Mathematical Stereology**. Memoirs No. 3, Department of Theoretical Statistics, University of Aarhus, Denmark, 1979. MR 0547508 | Zbl 0442.60019

[2] R. Coleman: **Line section sampling of Wicksell's corpuscles**. Acta Stereologica, 6 (1987), 33-36. Zbl 0619.60017

[3] E. N. Gilbert: **Random subdivision of space into crystals**. Ann. Math. Statistics, 33 (1962), 958-72. DOI 10.1214/aoms/1177704464 | MR 0144253

[4] A. M. Gokhale A. K. Jena: **Size distribution of grain-boundary precipitates**. Metallography 13 (1980), 307-17. DOI 10.1016/0026-0800(80)90028-2

[5] V. Horálek: **Statistical Models of Some Testing and Inspection Procedures of Products, Materials and Raw Materials**. (in Czech). Thesis, Charles University Praha, 1961.

[6] A. J. Jakeman R. S. Anderssen: **Abel type integral equation in stereology. I. General discussion**. J. Microscopy, 105 (1975), 121-33.

[7] J. W. Martin R. D. Doherty: **Stability of Microstructure in Metallic Systems**. Cambridge University Press, London, 1975.

[8] J. L. Meijering: **Interface area, edge length and number of vertices in crystal aggregates with random nucleation**. Philips Res. Rep. 8 (1953), 270-90. Zbl 0053.33401

[9] R. E. Miles: **The random division of space**. Suppl. Adv. Appl. Prob., 1972, 243-66. Zbl 0258.60015

[10] J. Møller: **Random tessellation in $R^d$**. Memoirs No. 9, Department of Theoretical Statistics, University of Aarhus, Denmark, 1986.

[11] S. A. Saltykov: **Stereometric Metallography**. 2nd. Ed., Metallurgizdat, Moscow, 1958.

[12] C. S. Smith L. Guttman: **Measurement of internal boundaries in three-dimensional structure by random sectioning**. Trans: AIME 197 (1953), 81 - 87.

[13] D. Stoyan W. S. Kendall J. Mecke: **Stochastic Geometry and Its Applications**. Akademie Verlag, Berlin, 1987. MR 0879119

[14] E. E. Underwood: **Quantitative Stereology**. Addison-Wesley, Reading, Mass., 1970.

[15] S. D. Wicksell: **The corpuscle problem. A mathematical study of a biometric problem**. Biometrika, 17 (1925), 84-99.