Simulation of a random field with given distribution of one-dimensional integral
-
Evgeniya G. Kablukova
und
Sergei M. Prigarin
Abstract
The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a layer 0 < z < H with given one-dimensional distribution and correlation function of the integral over coordinate z is solved. The gamma distribution with shape parameter ν and scale parameter θ is used in the work. An aggregate of n independent elementary horizontal layers of thickness h = H/n vertically shifted by a random value uniformly distributed in the interval (0, h) is considered as a basic model. For each elementary random field, the normalized correlation function of the corresponding integral over z coincides with the given one, the gamma distribution with parameters depending on the number of horizontal layers is used as a one-dimensional distribution. It is proved that for the constructed model the normalized correlation function of the integral over z coincides with the given normalized ‘horizontal’ correlation function, and the parameters of the one-dimensional distribution asymptotically converge to given values for n → + ∞, but the corresponding mathematical expectation and variance coincide exactly with given values. To extend the class of possible models, an additional randomization of the basic model is considered. In the conclusion the results of computations for a realistic version of the problem are presented.
Funding: The work was performed under the State Assignment 0315-2019-0002, partially supported by the Russian Foundation for Basic Research (projects 18–01–00149, 18–01–00356, 18–01–00609).
References
[1] A. A. Borovkov, Mathematical Statistics. Nauka, Novosibirsk, 1997 (in Russian).Suche in Google Scholar
[2] A. V. Ivanov, Convergence of distributions of functionals of measurable random fields. Ukr. Matem. Zh. 32 (1980), No. 1, 27–34 (in Russian).10.1007/BF01090462Suche in Google Scholar
[3] H. Kahn, Use of different Monte Carlo sampling techniques. In: Symposium on Monte Carlo Methods (Ed. H. A. Meyer). Wiley, New York, 1956, pp. 146–190.Suche in Google Scholar
[4] E. Lukach, Characteristic Functions. Nauka, Moscow, 1979 (in Russian).Suche in Google Scholar
[5] S. L. Marple, Jr. Digital Spectral Analysis with Applications. Prentice-Hall, Inc., Englewood Cliffs, New Jersey 07632, USA 1986.Suche in Google Scholar
[6] G. A. Mikhailov, Approximate models of random processes and fields. Zh. Vychisl. Matem. Matem. Fiz. 23 (1983), No. 3, 558–566 (in Russian).10.1016/S0041-5553(83)80097-4Suche in Google Scholar
[7] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modelling. Monte Carlo Methods. Akademiya, Moscow, 2006 (in Russian).Suche in Google Scholar
[8] V. A. Ogorodnikov and S. M. Prigarin, Numerical Modelling of Random Processes and Fields: Algorithms and Applications. VSP, Utrecht, 1996.10.1515/9783110941999Suche in Google Scholar
[9] V. A. Ogorodnikov, E. G. Kablukova and S. M. Prigarin, Stochastic models of atmospheric clouds structure. Stat. Paper59 (2018), No. 4, 1521–1532.10.1007/s00362-018-1036-7Suche in Google Scholar
[10] Z. A. Piranashvili, Some issues of statistical-probability simulation of random processes. In: Problems of Operational Research. Mitznereba, Tbilisi, 1966, pp. 53–91.Suche in Google Scholar
[11] S. M. Prigarin, Methods of Numerical Modeling of Random Processes and Fields. INM&MG SB RAS, Novosibirsk, 2005 (in Russian).Suche in Google Scholar
[12] M. Schafer, E. Bierwirth, A. Ehrlich, E. Jakel, F. Werner, and M. Wendish. Directional horizontal inhomogeneities of cloud optical thickness fields retrieved from ground-based and airborne spectral imaging. Atmos. Chem. Phys. 17 (2017), 2359– 2372.10.5194/acp-17-2359-2017Suche in Google Scholar
[13] M. Schafer, E. Bierwirth, A. Ehrlich, E. Jakel, F. Werner, and M. Wendish, Cloud optical thickness retrieved from horizontal fields of reflected solar spectral radiance measured with AisaEAGLE during VERDI campaign 2012, PANGAEA. DOI:10.1594/PANGAEA.87479810.1594/PANGAEA.874798Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section
- A note on the fast direct method for discrete elliptic problems
- Simulation of a random field with given distribution of one-dimensional integral
- A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media
- Approximate spectral models of random processes with periodic properties
- Automatic segmentation algorithms and personalized geometric modelling for a human knee
Artikel in diesem Heft
- Frontmatter
- Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section
- A note on the fast direct method for discrete elliptic problems
- Simulation of a random field with given distribution of one-dimensional integral
- A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media
- Approximate spectral models of random processes with periodic properties
- Automatic segmentation algorithms and personalized geometric modelling for a human knee
