TY - JOUR AU - Assefa, Genet Mekonnen AU - Baricz, Árpád TI - Infinite divisibility of the Whittaker distribution JF - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - P AM MATH SOC VL - 151 PY - 2023 IS - 12 SP - 5429 EP - 5442 PG - 14 SN - 0002-9939 DO - 10.1090/proc/16562 UR - https://m2.mtmt.hu/api/publication/34083413 ID - 34083413 LA - English DB - MTMT ER - TY - JOUR AU - Assefa, Genet Mekonnen AU - Baricz, Árpád TI - Exponential bounds for the logarithmic derivative of Whittaker functions JF - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - P AM MATH SOC VL - 151 PY - 2023 IS - 11 SP - 4867 EP - 4880 PG - 14 SN - 0002-9939 DO - 10.1090/proc/16549 UR - https://m2.mtmt.hu/api/publication/34083406 ID - 34083406 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Pogany, Tibor TI - Probabilistic and Analytical Aspects of the Symmetric and Generalized Kaiser–Bessel Window Function JF - CONSTRUCTIVE APPROXIMATION J2 - CONSTR APPROX VL - 58 PY - 2023 SP - 713 EP - 783 PG - 71 SN - 0176-4276 DO - 10.1007/s00365-023-09627-3 UR - https://m2.mtmt.hu/api/publication/33678790 ID - 33678790 AB - The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner’s semicircle, parabolic and n -sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Kumar, Pranav AU - Singh, Sanjeev TI - On starlikeness of regular Coulomb wave functions JF - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - P AM MATH SOC VL - 151 PY - 2023 IS - 6 SP - 2325 EP - 2338 PG - 14 SN - 0002-9939 DO - 10.1090/proc/16180 UR - https://m2.mtmt.hu/api/publication/33678786 ID - 33678786 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Bisht, Nitin AU - Singh, Sanjeev AU - Vijesh, Antony TI - Asymptotic and numerical aspects of the generalized Marcum function of the second kind JF - APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS J2 - APPL ANAL DISCR MATH VL - 16 PY - 2022 IS - 1 SP - 202 EP - 217 PG - 16 SN - 1452-8630 DO - 10.2298/AADM201001008B UR - https://m2.mtmt.hu/api/publication/32813106 ID - 32813106 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Bisht, Nitin AU - Singh, Sanjeev AU - Vijesh, V. Antony TI - Bounds for the generalized Marcum function of the second kind JF - RAMANUJAN JOURNAL J2 - RAMANUJAN J VL - 58 PY - 2022 IS - 1 SP - 1 EP - 21 PG - 21 SN - 1382-4090 DO - 10.1007/s11139-021-00440-9 UR - https://m2.mtmt.hu/api/publication/32220125 ID - 32220125 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Bisht, Nitin AU - Singh, Sanjeev AU - Vijesh, V. Antony TI - Functional Inequalities and Bounds for the Generalized Marcum Function of the Second Kind JF - RESULTS IN MATHEMATICS J2 - RES MATHEM VL - 76 PY - 2021 IS - 1 PG - 28 SN - 1422-6383 DO - 10.1007/s00025-021-01343-3 UR - https://m2.mtmt.hu/api/publication/32220086 ID - 32220086 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Bisht, Nitin AU - Singh, Sanjeev AU - Antony Vijesh, V. TI - The generalized Marcum function of the second kind: Monotonicity patterns and tight bounds JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 382 PY - 2021 SN - 0377-0427 DO - 10.1016/j.cam.2020.113093 UR - https://m2.mtmt.hu/api/publication/32220084 ID - 32220084 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Jankov Maširević, Dragana AU - Pogany, Tibor TI - Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals JF - MATHEMATICS J2 - MATHEMATICS-BASEL VL - 9 PY - 2021 IS - 2 SP - 129 PG - 12 SN - 2227-7390 DO - 10.3390/math9020129 UR - https://m2.mtmt.hu/api/publication/31808400 ID - 31808400 LA - English DB - MTMT ER - TY - JOUR AU - Baricz, Árpád AU - Nemes, Gergő TI - Asymptotic expansions for the radii of starlikeness of normalised Bessel functions JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 494 PY - 2021 IS - 2 PG - 11 SN - 0022-247X DO - 10.1016/j.jmaa.2020.124624 UR - https://m2.mtmt.hu/api/publication/31609652 ID - 31609652 LA - English DB - MTMT ER -