Stochastic Derivation of an Integral Equation for Probability Generating Functions

Panagiotis T. Artikis, Constantinos T. Artikis

Abstract


Functional, integral and differential equations of transformed probability generating functions are generally recognized as powerful analytical tools for establishing characterizations of discrete probability distributions. The present paper establishes a characterization of the distribution of an important integral part model by incorporating an integral equation based on three fundamental transformed probability generating functions. Interpretations of such a characterization in analyzing and implementing information risk frequency reduction operations are also established.

Keywords


Integral equation; Stochastic models; Risk theory

Full Text:

PDF

References


P. Artikis and C. Artikis, Stochastic derivation of an integral equation for characteristic functions, Journal of Informatics and Mathematical Sciences 1 (2009), 113-120.

T. Artikis, S. Loukas and D. Jerwood, A transformed geometric distribution in stochastic modelling, Mathematical and Computer Modelling 27 (1998), 43-51.

C. Goldie, A class of infinitely divisible distributions, Proc. Cambridge Phil. Soc. 63 (1967), 1141-1143.

R. Gupta, On the characterization of survival distributions in reliability by properties of their renewal densities, Communications in Statistics Theory and Methods 8 (1979), 685-697.

Y. Haimes, Risk Modelling, Assessment and Management, John Wiley & Sons, Inc., Hoboken, New Jersey, 2004.

J. Keilson and F. Steutel, Mixtures of distributions, moment inequalities and measures of exponentiality and normality, Ann. Probab. 2 (1974), 112-130.

N. Krishnaji, A characteristic property of the Yule distribution, Sankhya A 32 (1970), 343-346.

P. Medgyessy, On a new class of unimodal infinitely divisible distribution functions and related topics, Studia Scientiarum Mathematicarum Hungarica 2 (1967), 441-446.

F. Steutel and K. van Harn, Infinite Divisibility of Probability Distributions on the Real Line, Marcel Dekker, New York, 2003.




DOI: http://dx.doi.org/10.26713%2Fjims.v5i3.222

eISSN 0975-5748; pISSN 0974-875X