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Identities for divisor generating functions and their relations to a probability generating function
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Empirical probability generating function
Insurance: Mathematics and Economics, 1993Abstract A convenient approach to the statistical analysis of distributions for counts is possible using the empirical probability generating function. In this paper we give an overview of recent results and show the usefulness and advantages of this methodology.
Víctor Perez-Abreu
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Numerical inversion of probability generating functions
Operations Research Letters, 1992The authors provide an algorithm to approximate the discrete probability distribution \((p_ k)_{k\geq 0}\) when only the probability generating function \(G(z)=\sum_{k=0}^ \infty q_ k z^ k\), \(z\in\mathbb{C}\), \(| z|
Joseph Abate, Ward Whitt
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On Bounds for Probability Generating Functions
Australian Journal of Statistics, 1981SummaryBrook (1966) gave an upper bound for the moment generating function (m.g.f.) of a positive random variable (r.v.) in terms of its moments, and used this to obtain an upper bound for the probability generating function (p.g.f.) and hence the extinction probability of a simple branching process.
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Probability generating function of GPED2
Statistical Papers, 2007The Probability generating function of a random variable which has Generalized Polya Eggenberger Distribution of the second kind (GPED 2) is obtained. The probability density function of the range R, in random sampling from a uniform distribution on (k, l) and exponential distribution with parameter λ is obtained, when the sample size ...
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Belief Functions and Probability for General Spaces
2010 IEEE International Conference on Granular Computing, 2010This paper has two major contributions: 1) Shafer’s belief functions are extended from finite sets to general universes (sets). 2) Belief function theory on a universe with countable focal elements is interpreted as a probability theory on the product space $\Omega$ x [0; 1] A counter intuitive point of a belief function is its ignoring the impact of ...
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Introducing probability generating functions
The Mathematical Gazette, 1977The idea of a probability generating function seems to be a difficult one for sixth formers, and this may well be because the formalism is introduced too abruptly. The t or z or whatever letter is used in a p.g.f.
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Koenigs function and fractional iterates of probability generating functions
Sbornik: Mathematics, 2002The author studies various properties of Königs functions. A description of the class of Königs functions corresponding to probability generating functions embeddable in a one-parameter group of functional iterates is given. Cases of the probability generating functions with an interior fixed point, and an attracting boundary point are studied.
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