Date of Award
2024
Document Type
Open Access Dissertation
Degree Name
Doctor of Philosophy in Physics (PhD)
Administrative Home Department
Department of Physics
Advisor 1
Alex Kostinski
Committee Member 1
Jacek Borysow
Committee Member 2
Will Cantrell
Committee Member 3
Vladimir Tonchev
Abstract
The unifying theme of this thesis is the characterization of “perfect randomness,” i.e., independent and identically distributed (IID) stochastic processes as these are applied in physical science. Two specific and mathematically distinct applications are chosen: (i) Radar and optical polarimetry; (ii) Analysis of time series in meteorology. In (i), IID process of a special kind, namely, with a distribution defined by symmetry, is used to link its multivariate Gaussian density to uniformity on the Poincaré sphere. This “statistical ellipsometry” approach is then used to relate polarimetric mismatches or imbalances to ellipsometric variables and suitably chosen cross-correlation measures. In (ii), recently discovered and distribution-independent methods of data ranking are employed to examine temperature time series via the notion of the 2D cumulative distribution function in rank-time C(r, t) where the IID process again plays the central role in defining general signals. Several original analytic and computational results concerning C(r, t) are obtained.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.
Recommended Citation
Kestner, Dan, "APPLICATIONS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED (IID) RANDOM PROCESSES IN POLARIMETRY AND CLIMATOLOGY", Open Access Dissertation, Michigan Technological University, 2024.
Included in
Applied Statistics Commons, Optics Commons, Other Physics Commons, Theory and Algorithms Commons