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A Characterization of Exponential and Ordinary Generating Functions

2002
*
Journal of combinatorial theory. Series A
*

Rota once remarked that among all the possible

doi:10.1006/jcta.2001.3195
fatcat:aytmkftszje4nman57iqfxq24u
*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. ...##
###
Characteristic properties of generalized order statistics from exponential distributions

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 ...

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

2020
*
Pakistan Journal of Statistics and Operation Research
*

Some mathematicalproperties

doi:10.18187/pjsor.v16i2.3230
fatcat:qsb4nqyjqvbjvmdumeos3ovp6e
*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 ′ = ( ) = ∫ ∞ −∞ ( ) . ...##
###
The Generalized Odd Generalized Exponential Family of Distributions: Properties, Characterizations and Application

2021
*
Journal of Data Science
*

We introduce

doi:10.6339/jds.201707_15(3).0005
fatcat:mozf4w7oavdxhp72ul73a74434
*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. ...##
###
Type I General Exponential Class of distributions

2018
*
Pakistan Journal of Statistics and Operation Research
*

Some useful

doi:10.18187/pjsor.v14i1.2193
fatcat:raf66un755citkwtkfkzdli4ci
*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. ...##
###
Microcanonical foundation for systems with power-law distributions

2000
*
Journal of Physics A: Mathematical and General
*

Starting from microcanonical basis with the principle

doi:10.1088/0305-4470/33/48/311
fatcat:evtgvzawprd6ndiwacuujuworu
*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 ...##
###
The maximization of Tsallis entropy with complete deformed functions and the problem of constraints

2010
*
Physics Letters A
*

In order to obtain

doi:10.1016/j.physleta.2010.03.038
fatcat:mioqyco63feszcgxmeeyekvi6u
*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. ...##
###
Fixed Sequences for a Generalization of the Binomial Interpolated Operator and for some Other Operators
[article]

2012
*
arXiv
*
pre-print

Using

arXiv:1212.5195v1
fatcat:bcwypapwujfypia5e7nby4l7xy
*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. ...##
###
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

2018
*
International Journal of Advanced and Applied Sciences
*

First order

doi:10.21833/ijaas.2018.10.007
fatcat:2xn77lljsfgrri7rdsk5gjvtyq
*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*...##
###
On Popoviciu-Ionescu functional equation in one and several variables
[article]

2020
*
arXiv
*
pre-print

For

arXiv:2001.01951v1
fatcat:2ktlz533crh6lddwpqelzoa5bm
*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 ...##
###
Type II General Exponential Class of Distributions

2019
*
Pakistan Journal of Statistics and Operation Research
*

In this paper,

doi:10.18187/pjsor.v15i2.1699
fatcat:g6w7soe5uzhjhnpbpxjtj4uo2m
*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 ...##
###
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

2006
*
Physica A: Statistical Mechanics and its Applications
*

In these situations the dynamical behavior is exactly describable through infinite families

doi:10.1016/j.physa.2006.08.057
fatcat:7u53osshava3botnelxu4nkqvm
*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. ...##
###
Third-Order Computation and Bounded Arithmetic

2007
*
Journal of Logic and Computation
*

We describe

doi:10.1093/logcom/exm040
fatcat:jatxxmbvnbbjxes42ytkrujmme
*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*. ...
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