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A Characterization of Exponential and Ordinary Generating Functions

Dan Port
2002 Journal of combinatorial theory. Series A  
Rota once remarked that among all the possible generating functions that might be used to represent a, the ordinary and exponential generating functions are the most ubiquitous.  ...  We explore this and other applications of the generating function characterization property within probability and combinatorics. © 2002 Elsevier Science (USA)  ...  ACKNOWLEDGMENTS The problem of characterizing exponential and ordinary generating functions was suggested to me by the late G. C. Rota.  ... 
doi:10.1006/jcta.2001.3195 fatcat:aytmkftszje4nman57iqfxq24u

Characteristic properties of generalized order statistics from exponential distributions

Udo Kamps, Ursula Gather
1997 Applicationes Mathematicae  
Exponential distributions are characterized by distributional properties of generalized order statistics.  ...  These characterizations include known results for ordinary order statistics and record values as particular cases. 1991 Mathematics Subject Classification: 60E05, 62E10, 62E15.  ...  In this paper we present characterizations of exponential distributions via distributional properties of generalized order statistics including the known results for ordinary order statistics and record  ... 
doi:10.4064/am-24-4-383-391 fatcat:azjnoclumverrpcn6fdeh3muom

The Poisson Topp Leone Generator of Distributions for Lifetime Data: Theory, Characterizations and Applications

Faton Merovci, Haitham Yousof, G. G Hamedani
2020 Pakistan Journal of Statistics and Operation Research  
Some mathematicalproperties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived.  ...  We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al.,  ...  Moments, incomplete moments and generating function The th ordinary moment of is given by ′ = ( ) = ∫ ∞ −∞ ( ) .  ... 
doi:10.18187/pjsor.v16i2.3230 fatcat:qsb4nqyjqvbjvmdumeos3ovp6e

The Generalized Odd Generalized Exponential Family of Distributions: Properties, Characterizations and Application

Morad Alizadeh, Indranil Ghosh, Haitham M. Yousof, Mahdi Rasekhi, G.G. Hamedani
2021 Journal of Data Science  
We introduce a new class of distributions called the generalized odd generalized exponential family.  ...  Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Ŕnyi, Shannon and q-entropies, order statistics and probability  ...  , probability weighted moments, residual life and reversed residual life functions, ordinary and incomplete moments, generating function and order statistics.  ... 
doi:10.6339/jds.201707_15(3).0005 fatcat:mozf4w7oavdxhp72ul73a74434

Type I General Exponential Class of distributions

Dr. G.G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi
2018 Pakistan Journal of Statistics and Operation Research  
Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented.  ...  We introduce a new family of continuous distributions and study the mathematical properties of the new family.  ...  Acknowledgements The authors are grateful to Professor Nadeem Shafique Butt and the reviewers for their comments and suggestions which certainly improved the presentation of the content of this work.  ... 
doi:10.18187/pjsor.v14i1.2193 fatcat:raf66un755citkwtkfkzdli4ci

Microcanonical foundation for systems with power-law distributions

Sumiyoshi Abe, A K Rajagopal
2000 Journal of Physics A: Mathematical and General  
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems  ...  In the limit q → 1, e x q ( ) converges to the ordinary exponential function.  ...  value a , may be understood from the point of view that the step function is of discrete topology and therefore can remain invariant under continuous deformation of the exponential function in the integrand  ... 
doi:10.1088/0305-4470/33/48/311 fatcat:evtgvzawprd6ndiwacuujuworu

The maximization of Tsallis entropy with complete deformed functions and the problem of constraints

Thomas Oikonomou, G. Baris Bagci
2010 Physics Letters A  
In order to obtain a complete definition of q-generalized functions, we calculate the dual mapping function, which is found equal to the otherwise ad hoc duality relation between the ordinary and escort  ...  Motivated by this fact, we show that the maximization of the Tsallis entropy with the complete q-logarithm and q-exponential implies the use of the ordinary probability distributions instead of escort  ...  Tirnakli for a careful reading of the manuscript. GBB was supported by TUBITAK (Turkish Agency) under the Research Project number 108T013.  ... 
doi:10.1016/j.physleta.2010.03.038 fatcat:mioqyco63feszcgxmeeyekvi6u

Fixed Sequences for a Generalization of the Binomial Interpolated Operator and for some Other Operators [article]

Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
2012 arXiv   pre-print
Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the Generalized Binomial operator.  ...  Finally we find the eigen-sequences for the mutual compositions of the operators Interpolated Invert, Generalized Binomial and Revert.  ...  Acknowledgements The authors would like to thank the referee for the valuable and interesting comments and suggestions which have improved this paper.  ... 
arXiv:1212.5195v1 fatcat:bcwypapwujfypia5e7nby4l7xy

Page 4172 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
, and then some characterizations of exponential stability for a family of Co semigroups are deduced from this formula.  ...  The authors present a detailed study of the asymptotic Laplace transformation; in one of the main results a characterization of analytic functions which are asymptotic Laplace transforms of generalized  ... 

Ordinary differential equations of probability functions of convoluted distributions

Hilary I. Okagbue, Muminu O. Adamu, Timothy A. Anake
2018 International Journal of Advanced and Applied Sciences  
First order ordinary differential equations whose solutions were the PDF, SF, HF and RHF for the probability functions of CPCED by the use of differential calculus.  ...  The difficulty of obtaining the ODE for the probability functions of the DPCED was due to the different parameters that characterize the distribution.  ...  Conclusion First order ordinary differential equations whose solutions were the PDF, SF, HF and RHF for the probability functions of constant parameter convoluted exponential distribution by the use of  ... 
doi:10.21833/ijaas.2018.10.007 fatcat:2xn77lljsfgrri7rdsk5gjvtyq

On Popoviciu-Ionescu functional equation in one and several variables [article]

J. M. Almira
2020 arXiv   pre-print
For functions of a single variable, our solution is different from the existing ones and, for functions of several variables, our solution is, as far as we know, the first one that exists.  ...  We present a solution to the equation both for the one-dimensional and the higher-dimensional cases, which is based on a generalization of Radó's theorem to distributions in a higher dimensional setting  ...  Furthermore, for every countable infinite field K there exists a function f : K 2 → K which is an ordinary algebraic polynomial function separately in each variable and is not a generalized polynomial  ... 
arXiv:2001.01951v1 fatcat:2ktlz533crh6lddwpqelzoa5bm

Type II General Exponential Class of Distributions

G. G. Hamedani, Mahdi Rasekhi, Sayed Najibi, Haitham M. Yousof, Morad Alizadeh
2019 Pakistan Journal of Statistics and Operation Research  
In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution.  ...  Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived  ...  We provide a comprehensive treatment of some of its mathematical properties including ordinary and incomplete moments, generating function, asymptotics, order statistics and the QS order, moment of residual  ... 
doi:10.18187/pjsor.v15i2.1699 fatcat:g6w7soe5uzhjhnpbpxjtj4uo2m

Page 2974 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
function and g is a smooth vector-valued function, has a unique generalized solution in an algebra of periodic generalized functions.  ...  It is shown that the ordinary differential equation x’ = A(t)x + uf (t)+g(t,x), where A is a matrix-valued periodic generalized function, w is a generalized constant, f is a periodic vector-valued generalized  ... 

Routes to chaos, universality and glass formation

Fulvio Baldovin
2006 Physica A: Statistical Mechanics and its Applications  
In these situations the dynamical behavior is exactly describable through infinite families of Tsallis' q-exponential functions.  ...  Specifically, the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest is corroborated for such a system.  ...  Stella and B. Marcone for useful remarks, and M. Zamberlan for daily support.  ... 
doi:10.1016/j.physa.2006.08.057 fatcat:7u53osshava3botnelxu4nkqvm

Third-Order Computation and Bounded Arithmetic

A. Skelley
2007 Journal of Logic and Computation  
We describe a natural generalization of ordinary computation to a third-order setting and give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity  ...  We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the EXP-time hierarchy in the third-order setting.  ...  See [3] for a previous recursion-theoretic characterization of the exponential-time number functions.  ... 
doi:10.1093/logcom/exm040 fatcat:jatxxmbvnbbjxes42ytkrujmme
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