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Everything about Probability integral transform
Probability theory operation
In probability theory, the probability integral transform relates to the result that data values that are modeled as being random variables from any given continuous distribution can be converted to random variables having a standard uniform distribution. This holds exactly provided that the distribution being used is the true distribution of the random variables; if the distribution is one fitted to the data, the result will hold approximately in large samples. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Probability integral transformA 5-minute orientation
- Skim a recent paper: Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear dataInfluential work since 2022
- Pick up a classic book: Mittag-Leffler Functions, Related Topics and ApplicationsThe most-reprinted book on the subject
- Read the landmark paper: The Probability Integral Transform and Related ResultsCited 183 times
- Go sideways: Cumulative distribution functionA closely related topic
- Go sideways: Inverse transform samplingA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Probability Integral Transform and Related Results
Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions
Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach
Calibration diagnostics for point process models via the probability integral transform
Sequential Probability Forecasts and the Probability Integral Transform
Double Probability Integral Transform Residuals for Regression Models with Discrete Outcomes
On integration, substitution and the probability integral transform
Probability transformation method for the evaluation of derivative, integral and Fourier transform of some stochastic processes
🆕 Influential since 2022
đź“š Books worth reading
Mittag-Leffler Functions, Related Topics and ApplicationsRudolf Gorenflo, Anatoly A. Kilbas · 2014
Algebraic structures and operator calculusPhilip J. Feinsilver, P. Feinsilver · 1899
Generalized Integral Transforms In Mathematical FinanceAndrey Itkin, Alexander Lipton · 2021
Asymptotical Behaviour of Laplace-Stiltjes IntegralsMyroslav Sheremeta · 2010
Transform techniques for probability modelingWalter C. Giffin · 1975
Advanced Integration TheoryCorneliu Constantinescu · 1998
Approximation by multivariate singular integralsGeorge A. Anastassiou · 2011
Approximation Of Additive Convolutionlike Operators Real Calgebra ApproachVictor Didenko · 2008
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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