Probability distribution built by Prabhakar function. Related Turán and Laguerre inequalities

DOI10.1080/10652469.2016.1201817zbMath1357.26044arXiv1605.01981OpenAlexW2963099118MaRDI QIDQ5506798

Živorad Tomovski, Tibor K. Pogány

Publication date: 16 December 2016

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01981

zbMATH Keywords

momentsPrabhakar functionLaguerre inequalityfunctional boundsrecurrence identitiesthree-parameter Mittag-Leffler functionTuránian difference

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Probability distributions: general theory (60E05) Mittag-Leffler functions and generalizations (33E12) Inequalities for sums, series and integrals (26D15)

Related Items

Analytical treatment of regularized Prabhakar fractional differential equations by invariant subspaces, A practical guide to Prabhakar fractional calculus, Asymptotic results for families of random variables having power series distributions, Asymptotic results for a multivariate version of the alternative fractional Poisson process, The Prabhakar or three parameter Mittag-Leffler function: theory and application, The Havriliak–Negami relaxation and its relatives: the response, relaxation and probability density functions, Integrals of ratios of Fox-Wright and incomplete Fox-Wright functions with applications, Prabhakar Lévy processes, Flexible models for overdispersed and underdispersed count data, Numerical approximation to Prabhakar fractional Sturm-Liouville problem, Finiteness conditions for performance indices in generalized fractional-order systems defined based on the regularized Prabhakar derivative

Cites Work

• Generalization of the fractional Poisson distribution
• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• A class of correlated weighted Poisson processes
• A class of weighted Poisson processes
• Fractional Poisson processes and related planar random motions
• Fractional Poisson process
• Laplace type integral expressions for a certain three-parameter family of generalized Mittag-Leffler functions with applications involving complete monotonicity
• Large deviations for fractional Poisson processes
• A class of Hurwitz-Lerch zeta distributions and their applications in reliability
• Integral and computational representations of the extended Hurwitz–Lerch zeta function
• Some applications of the fractional Poisson probability distribution
• Mittag-Leffler Functions, Related Topics and Applications
• On inequalities of the Turán type