Functional summary statistics for the Johnson–Mehl model

References

• Johnson WA, Mehl RF. Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Eng. 1939;135:416–458.
   Google Scholar
• Chiu SN, Stoyan D, Kendall WS, Mecke J. Stochastic geometry and its applications. 3rd ed. Chichester: John Wiley & Sons; 2013.
   Google Scholar
• Okabe A, Boots B, Sugihara K, Chiu SN. Spatial tessellations. Concepts and applications of Voronoi diagrams. 2nd ed. Chichester: Wiley; 2000.
   Google Scholar
• Møller J. Lectures on random Voronoi tessellations. Lecture Notes in Statistics 87. New York: Springer-Verlag; 1994.
   Google Scholar
• Kolmogorov AN. On the statistical theory of the crystallization of metals. Bull Acad Sci USSR, Math Ser. 1937;1: 355–359.
   Google Scholar
• Frost HJ, Thompson CV, Walton DT. Simulation of thin film grain structures–II. Abnormal grain growth. Acta Metall et Mater. 1992;40:779–793. doi: 10.1016/0956-7151(92)90020-F
   Google Scholar
• Kenkel NC. Spatial competition models for plant populations. COENOSES. 1990;5:149–158.
   Google Scholar
• Boots B, Okabe A, Thomas R, editors. Modelling geographical systems: statistical and computational applications. Dordrecht: Kluwer Academic Publishers; 2003.
   Google Scholar
• Vanderbei R, Shepp L. A probabilistic model for the time to unravel a strand of DNA. Stoch Models. 1988;4:299–314. doi: 10.1080/15326348808807082
   Google Scholar
• Cowan R, Chiu SN, Holst L. A limit theorem for the replication time of a DNA molecule. J Appl Probab. 1995;32: 296–303. doi: 10.2307/3215289
   Web of Science ®Google Scholar
• Quine MP, Robinson J. A linear random growth model. J Appl Probab. 1990;27:499–509. doi: 10.2307/3214536
   Web of Science ®Google Scholar
• Quine MP, Robinson J. Estimation for a linear growth model. Stat Probab Lett. 1992;15:293–297. doi: 10.1016/0167-7152(92)90165-2
   Web of Science ®Google Scholar
• Bennett MR, Robinson J. Probabilistic secretion of quanta from nerve terminals at synaptic sites on muscle cells: non-uniformity, autoinhibition and the binomial hypothesis. Proc R Soc Lond Ser B, Biol Sci. 1990;239:1049–1052. doi: 10.1098/rspb.1990.0020
   Web of Science ®Google Scholar
• Chiu SN, Quine MP, Stewart M. Nonparametric and parametric estimation for a linear germination-growth model. Biometrics. 2000;56:755–760. doi: 10.1111/j.0006-341X.2000.00755.x
   PubMed Web of Science ®Google Scholar
• Molchanov IS, Chiu SN. Smoothing techniques and estimation methods for nonstationary Boolean models with applications to coverage processes. Biometrika. 2000;87:265–283. doi: 10.1093/biomet/87.2.265
   Web of Science ®Google Scholar
• Chiu SN, Molchanov IS, Quine MP. Maximum likelihood estimation for germination-growth processes with application to neurotransmitters data. J Stat Comput Simul. 2003;73:725–732. doi: 10.1080/0094965031000078855
   Web of Science ®Google Scholar
• Wolk CP. Formation of one-dimensional patterns by stochastic processes and by filamentous blue-green algae. Dev Biol. 1975;46:370–382. doi: 10.1016/0012-1606(75)90113-X
   PubMed Web of Science ®Google Scholar
• Kayser K, Stute H. Minimum spanning tree, Voronoi's tessellation and Johnson–Mehl diagrams in human lung carcinoma. Pathol Res Pract. 1989;185:729–734. doi: 10.1016/S0344-0338(89)80228-6
   PubMed Web of Science ®Google Scholar
• Meijering JL. Interface area, edge length, and number of vertices in crystal aggregates with random nucleation. Philips Res Rep. 1953;8:270–290.
   Google Scholar
• Gilbert EN. Random subdivisions of space into crystals. Ann Math Stat. 1962;33:958–972. doi: 10.1214/aoms/1177704464
   Google Scholar
• Miles RE. The random subdivision of space. Suppl Adv Appl Probab. 1972;4:243–266. doi: 10.2307/1425985
   Google Scholar
• Horálek V. A note on the time-homogeneous Johnson–Mehl tessellation. Adv Appl Probab. 1988;20:684–685. doi: 10.2307/1427043
   Web of Science ®Google Scholar
• Horálek V. ASTM grain-size model and related random tessellation models. Mater Charact. 1990;25:263–284. doi: 10.1016/1044-5803(90)90057-Q
   Web of Science ®Google Scholar
• Møller J. Random Johnson–Mehl tessellations. Adv Appl Probab. 1992;24:814–844. doi: 10.2307/1427714
   Web of Science ®Google Scholar
• Møller J. Generation of Johnson–Mehl crystals and comparative analysis of models for random nucleation. Adv Appl Probab. 1995;27:367–383. doi: 10.2307/1427831
   Web of Science ®Google Scholar
• Gabriel E, Diggle PJ. Second-order analysis of inhomogeneous spatio-temporal point process data. Statist Neerlandica. 2009;63:43–51. doi: 10.1111/j.1467-9574.2008.00407.x
   Web of Science ®Google Scholar
• Møller J, Ghorbani M. Aspects of second-order analysis of structured inhomogeneous spatio-temporal point processes. Statist Neerlandica. 2012;66:472–491. doi: 10.1111/j.1467-9574.2012.00526.x
   Web of Science ®Google Scholar
• Mecke J. Stationäre zufällige Maße auf lokalkompakten Abelschen Gruppen. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1967;9:36–58. doi: 10.1007/BF00535466
   Web of Science ®Google Scholar
• Møller J, Waagepetersen RP. Statistical inference and simulation for spatial point processes. Boca Raton, FL: Chapman and Hall/CRC; 2004.
   Google Scholar
• Frost HJ, Thompson CV. The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures. Acta Metall Mater. 1987;35:529–540. doi: 10.1016/0001-6160(87)90258-6
   Google Scholar
• Chiu SN. Limit theorems for the time of completion of Johnson–Mehl tessellations. Adv Appl Probab. 1995;27: 889–910. doi: 10.2307/1427927
   Web of Science ®Google Scholar
• Daley DJ, Vere-Jones D. An introduction to the theory of point processes. Volume I: elementary theory and methods. 2nd ed. New York: Springer-Verlag; 2003.
   Google Scholar
• Li S. Concise formulas for the area and volume of a hyperspherical cap. Asian J Math Stat. 2011;4:66–70. doi: 10.3923/ajms.2011.66.70
   Google Scholar
• Gelfand AE, Diggle PJ, Guttorp P, Fuentes M. Handbook of spatial statistics. Boca Raton, FL: CRC Press; 2010.
   Google Scholar
• Stoyan D, Stoyan H. Estimating pair correlation functions of planar cluster processes. Biom J. 1996;38: 259–271. doi: 10.1002/bimj.4710380302
   Web of Science ®Google Scholar
• Baddeley A, Møller J, Waagepetersen R. Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statist Neerlandica. 2000;54:329–350. doi: 10.1111/1467-9574.00144
   Web of Science ®Google Scholar
• Ripley BD. The second-order analysis of stationary point processes. J Appl Probab. 1976;13:255–266. doi: 10.2307/3212829
   Web of Science ®Google Scholar
• Ripley BD. Modelling spatial patterns (with discussion). J R Stat Soc Ser B. 1977;39:172–212.
   Google Scholar
• Thomson PC, Lavidis NA, Robinson J, Bennett MR. Probabilistic secretion of quanta at somatic motor-nerve terminals: the fusion-pore model, quantal detection and autoinhibition. Philos Trans: Biol Sci. 1995;349: 197–214. doi: 10.1098/rstb.1995.0103
   PubMed Web of Science ®Google Scholar
• Holst L, Quine MP, Robinson J. A general stochastic model for nucleation and linear growth. Ann Appl Probab. 1996;6:903–921. doi: 10.1214/aoap/1034968233
   Google Scholar