Zobrazeno 1 - 10
of 153
pro vyhledávání: '"G. Pakes"'
Autor:
Anthony G. Pakes
Publikováno v:
Axioms, Vol 13, Iss 2, p 115 (2024)
The deterministic SIR model for disease spread in a closed population is extended to allow infected individuals to recover to the susceptible state. This extension preserves the second constant of motion, i.e., a functional relationship of susceptibl
Externí odkaz:
https://doaj.org/article/7af55b79bf364bd591fa37e4c3e1da6a
Autor:
Anthony G. Pakes
Publikováno v:
Axioms, Vol 11, Iss 11, p 584 (2022)
Concepts of infinitely divisible distributions are reviewed and applied to mutant number distributions derived from the Lea-Coulson and other models which describe the Luria-Delbrück fluctuation test. A key finding is that mutant number distribution
Externí odkaz:
https://doaj.org/article/6d028da2b9f846a5995f3a61ff5b1318
Autor:
Anthony G. Pakes
Publikováno v:
Journal of Statistical Distributions and Applications, Vol 8, Iss 1, Pp 1-33 (2021)
A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium law of a perturbed version of the Feller me
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::953eeacad98bd109a2fdd17bd7f4d862
https://doaj.org/article/cc4bdf8e7254445d8522de2a2e5b056e
https://doaj.org/article/cc4bdf8e7254445d8522de2a2e5b056e
Autor:
Anthony G. Pakes
Publikováno v:
Journal of Probability and Statistics, Vol 2017 (2017)
This paper studies aspects of the Siegmund dual of the Markov branching process. The principal results are optimal convergence rates of its transition function and limit theorems in the case that it is not positive recurrent. Additional discussion is
Externí odkaz:
https://doaj.org/article/eb66521c141f4e49989463ea669d9092
Publikováno v:
Analysis and Applications. 18:447-468
Large deviation rates are determined for quantities associated with a Markov branching process [Formula: see text] having offspring mean [Formula: see text] and split rate [Formula: see text]. The principal quantities examined are [Formula: see text]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b2d53a776fb5c7c7bec1acf790a5ac4c
https://doi.org/10.1142/s0219530519500209
https://doi.org/10.1142/s0219530519500209
Autor:
Anthony G. Pakes
Publikováno v:
Journal of Theoretical Probability. 33:361-395
The martingale limit law of the supercritical continuous time and state branching process either is compound Poisson or self-decomposable. This paper explores some general aspects of the latter case. A fundamental question for the latter case is whet
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::521a76bf47333b913f127c2ef4c7196a
https://doi.org/10.1007/s10959-019-00886-0
https://doi.org/10.1007/s10959-019-00886-0
Autor:
Anthony G. Pakes
Publikováno v:
Statistics & Probability Letters. 139:53-60
This paper offers a new proof that the principal Lambert W -function W ( s ) is a Bernstein function. The proof derives from a known integral evaluation and leads to a more detailed description of W ( s ) as a Thorin–Bernstein function with a real-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d18f5aaccb6db4dba3e796feed216818
https://doi.org/10.1016/j.spl.2018.03.015
https://doi.org/10.1016/j.spl.2018.03.015
Autor:
Anthony G. Pakes
Publikováno v:
Bulletin of the American Mathematical Society. 54:537-540
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f90801a11766c6674588efbe1eaf725
https://doi.org/10.1090/bull/1574
https://doi.org/10.1090/bull/1574
Autor:
Anthony G. Pakes
Publikováno v:
Probability and Mathematical Statistics. 41
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ab68e2453c87dc417fe8d8264379b636
https://doi.org/10.37190/0208-4147.41.1.5
https://doi.org/10.37190/0208-4147.41.1.5
Autor:
Anthony G. Pakes
Publikováno v:
Journal of Mathematical Analysis and Applications. 499:125008
A certain subfamily of discrete compound Poisson laws is known to be characterised in terms of an affine relation linking the probability masses with those of its jump law. We show that the continuous version of this relation leads to the so-called G
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f8054cb4dcca32913942a0c6bef2cc80
https://doi.org/10.1016/j.jmaa.2021.125008
https://doi.org/10.1016/j.jmaa.2021.125008