STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Stohastika sa primenama:
https://miteam.mi.sanu.ac.rs/asset/n4AMxqgneB2qxFuT2

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Plan rada seminara Stohastika sa primenama za MAJ 2025.

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Četvrtak, 08.05.2025. u 18:00, Online
Tibor K. Pogány, Institute of Applied Mathematics, Óbuda University, Budapest, Hungary
ON PDF AND CDF OF RICE-MIDDLETON MODEL
The probability density function in the Rice-Middleton model, which describes the behaviour of the single sinusoidal random signal combined with Gaussian noise was recently considered by Trifonov. He has found its Neumann-Bessel series form, which motivated a set of equivalent, but more elegant and numerically superior representations which are expressed in several mutually independent ways: firstly, with the aid of an integral representation of the modified Bessel function of the first kind of integer order; secondly, by a hyperbolic cosine differential operator; thirdly, applying the Grünwald-Letnikov fractional derivative and finally using the Srivastava-Daoust S function, by a related linear ODE. The cumulative distribution functions are also described in all these cases, and also using the Nuttall Q-function.
An associated new probability distribution is introduced which cumulative distribution function and the raw moments of general real order are obtained, whilst the characteristic function's power series form is inferred and modality result was also found. The exposition ends with a discussion in which by-product summations are given for the considered Neumann series of the second type built by modified Bessel functions of the first kind having integer order.

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Četvrtak, 22.05.2025. u 11:00, Online
Dragana Jankov Maširević, School of Applied Mathematics and Informatics, University of Osijek, Croatia
DETAILED STUDY OF MCKAY I BESSEL DISTRIBUTION
The probability distributions involving Bessel functions have caught the interest of many mathematicians and first results about this topic can be traced back to the early work of A. T. McKay in 1932 and R. G. Laha in 1954 who considered two classes of continuous distributions called Bessel function distributions, one, which building block is the modified Bessel function of the first kind I of the order, and another which is defined by the modified Bessel function of the second kind K. This talk is devoted the first type distribution.
Bearing in mind various applications of random variable distributed according to the McKay I Bessel law the appropriate cumulative distribution functions (abbr. d.f.) has been considered in mathematical literature and the main aim of this talk is to present several new formulae for such d.f.
First set of formulae are given in terms of incomplete generalized Fox-Wright function while the other expressions include Exton generalized hypergeometric X function of two variables, and also the incomplete Lipschitz-Hankel integral for the modified Bessel function of the first kind. Furthermore, bearing in mind an increasing popularity of the fractional calculus we will consider several new representation formulae for d.f. of the McKay I Bessel distribution including the Grünwald-Letnikov fractional derivative. New representations for such d.f. will be derived using two versions of the second mean-value theorems for definite integrals and properties of Lambert W function, as well. Our newly obtained formulae can be more convenient for practical purposes, since in some problems computation of the observed d.f. can be a bit challenging. In addition, we will observe results concerning log-concavity for the McKay I law and we resolve the M-determinacy, unimodality and some mode results of the considered distribution.

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