scholarly journals From Invariance Under Binomial Thinning to Unification of the Cauchy and the Gołąb–Schinzel-Type Equations

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Karol Baron ◽  
Jacek Wesolowski
Keyword(s):  
Power Series ◽  
Functional Equations ◽  
Probability Distributions ◽  
Binomial Thinning ◽  
Additive Form

AbstractWe point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Gołąb–Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

Burmann-series distributions and approximation operators

2005 ◽  
Vol 42 (4) ◽  
pp. 355-369
Author(s):  
J. P. King
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Operators ◽  
Real Functions

Burmann series are used to give probability distributions which generalize the known class of distributions given by power series. Positive linear operators associated with Burmann-series distribution are described. Convergence of these operators to continuous real functions is studied. Examples are discussed.

The Orthogonal Polynomials of Power Series Probability Distributions and Their Uses

Biometrika ◽  
1966 ◽  
Vol 53 (1/2) ◽  
pp. 121
Author(s):  
D. F. I van Heerden ◽  
H. T. Gonin
Keyword(s):  
Power Series ◽  
Orthogonal Polynomials ◽  
Probability Distributions

scholarly journals The T–R {Y} power series family of probability distributions

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Patrick Osatohanmwen ◽  
Francis O. Oyegue ◽  
Sunday M. Ogbonmwan
Keyword(s):  
Power Series ◽  
Probability Distributions

scholarly journals Families of Commuting Formal Power Series and Formal Functional Equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Harald Fripertinger ◽  
Ludwig Reich
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Formal Power Series ◽  
Functional Equations ◽  
Normal Forms ◽  
Type I ◽  
Formal Power

AbstractIn this paper we describe families of commuting invertible formal power series in one indeterminate over 𝔺, using the method of formal functional equations. We give a characterization of such families where the set of multipliers (first coefficients) σ of its members F (x) = σ x + . . . is infinite, in particular of such families which are maximal with respect to inclusion, so called families of type I. The description of these families is based on Aczél–Jabotinsky differential equations, iteration groups, and on some results on normal forms of invertible series with respect to conjugation.

Sign in / Sign up

Export Citation Format

Share Document