Formulas for characteristic function and moment generating functions of beta type distribution

DOI10.1007/s13398-022-01229-1zbMath1493.62258OpenAlexW4220933410WikidataQ113899229 ScholiaQ113899229MaRDI QIDQ2121665

Yilmaz Simsek, Fusun Yalcin

Publication date: 4 April 2022

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-022-01229-1

zbMATH Keywords

beta functiongamma functionBernstein polynomialsgenerating functionStirling numbersmoment generating functiondigamma functionbeta distribution

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Order statistics; empirical distribution functions (62G30) Characteristic functions; other transforms (60E10) Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Probability distributions: general theory (60E05) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Special sequences and polynomials (11B83) Real polynomials: analytic properties, etc. (26C05) Probabilistic methods for one variable harmonic analysis (42A61)

Cites Work

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• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions
• A New Nonparametric Estimation Method of the Variance in Heteroscedastic Model
• Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers
• Formulas derived from moment generating functions and Bernstein polynomials

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