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Everything about Probability generating function
Power series derived from a discrete probability distribution
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are often employed for their succinct description of the sequence of probabilities Pr(X = i) in the probability mass function for a random variable X, and to make available the well-developed theory of power series with non-negative coefficients. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Probability generating functionA 5-minute orientation
- Skim a recent paper: Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation ApproachInfluential work since 2022
- Pick up a classic book: Time Series AnalysisThe most-reprinted book on the subject
- Read the landmark paper: Numerical inversion of probability generating functionsCited 179 times
- Go sideways: Central limit theoremA closely related topic
- Go sideways: Probability density functionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Numerical inversion of probability generating functions
The probability generating functional
The information generating function of a probability distribution (Corresp.)
Choice probability generating functions
Goodness of fit for the poisson distribution based on the probability generating function
Tests of fit for discrete distributions based on the probability generating function
Use of an empirical probability generating function for testing a Poisson model
Empirical probability generating function
🆕 Influential since 2022
Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach
circGPA: circRNA functional annotation based on probability-generating functions
Alternating minimization algorithm with a probability generating function-based distance measure
On Integral Representations Involving the Probability Generating Function for Inverse Moments of Positive Discrete Random Variables
Efficiency, accuracy and robustness of probability generating function based parameter inference method for stochastic biochemical reactions
đź“š Books worth reading
Time Series AnalysisGeorge E. P. Box, Gwilym M. Jenkins · 1970
Stochastic processes and functional analysisM. M. Rao, Randall J. Swift · 2004- 📕Multivariate Kernel Smoothing and Its ApplicationsJosé E. Chacón, Tarn Duong · 2018
Bayesian methods for finite population samplingMalay Ghosh · 1997
Approximate Iterative AlgorithmsAnthony Louis Almudevar · 2014
Isometries on Banach spacesRichard J Fleming, Richard J. Fleming · 2002
A history of inverse probabilityAndrew I. Dale · 1991
Concise Introduction to Basic Real AnalysisHemen Dutta, P. N. Natarajan · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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