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Open AccessFeature PaperArticle

A New Class of Symmetric Beta Type Distributions Constructed by Means of Symmetric Bernstein Type Basis Functions

Department of Mathematics, Faculty of Science University of Akdeniz, TR-07058 Antalya, Turkey
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Symmetry 2020, 12(5), 779; https://doi.org/10.3390/sym12050779
Received: 14 April 2020 / Revised: 24 April 2020 / Accepted: 6 May 2020 / Published: 7 May 2020
The main aim of this paper is to define and investigate a new class of symmetric beta type distributions with the help of the symmetric Bernstein-type basis functions. We give symmetry property of these distributions and the Bernstein-type basis functions. Using the Bernstein-type basis functions and binomial series, we give some series and integral representations including moment generating function for these distributions. Using generating functions and their functional equations, we also give many new identities related to the moments, the polygamma function, the digamma function, the harmonic numbers, the Stirling numbers, generalized harmonic numbers, the Lah numbers, the Bernstein-type basis functions, the array polynomials, and the Apostol–Bernoulli polynomials. Moreover, some numerical values of the expected values for the logarithm of random variable are given. View Full-Text
Keywords: Bernstein basis functions; moment generating function; Stirling numbers; digamma function; symmetric beta distributions; Apostol–Bernoulli polynomials; symmetry property random variable; harmonic numbers; Lah numbers Bernstein basis functions; moment generating function; Stirling numbers; digamma function; symmetric beta distributions; Apostol–Bernoulli polynomials; symmetry property random variable; harmonic numbers; Lah numbers
MDPI and ACS Style

Yalcin, F.; Simsek, Y. A New Class of Symmetric Beta Type Distributions Constructed by Means of Symmetric Bernstein Type Basis Functions. Symmetry 2020, 12, 779.

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