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Understanding Transformer-Based Classifications of Medical Text Using a Large Language Model for the Attribution of Feature Importance: Proof-of-Concept Algorithm Development and Validation Study. [PDF]
JMIR Med InformZhou F +6 more
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Identities for divisor generating functions and their relations to a probability generating function
Identities for divisor generating functions and their relations to a probability generating functionopenaire +1 more source
Distribution Function, Probability Generating Function and Archimedean Generator [PDF]
Symmetry, 2020 Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating ...
Weaam Alhadlaq, Abdulhamid Alzaid
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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 Pérez-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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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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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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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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Probability Distributions and Generating Functions
2012The p-dimensional random variable \(X = {[{\textbf{X} }_{1},\ldots,{X}_{p}]}^{\mbox{ T}}\) has a normal distribution, denoted \({\mbox{ N}}_{p}(\boldsymbol\mu,\boldsymbol\Sigma )\), with mean \(\boldsymbol\mu = {[{\mu }_{1},\ldots,{\mu }_{p}]}^{\mbox{ T}}\) and p ×p variance–covariance matrix \(\Sigma \) if its density is of the form $$p(\textbf{x}
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