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Everything about Probability density function
Description of continuous random distribution
In probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given point in the sample space can be interpreted as providing a "relative probability" that the value of the random variable would be equal to that point. Probability density is the probability per unit length, in other words. The (absolute) probability for a continuous random variable to take on any particular value is zero. Therefore, the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one point compared to the other. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Probability density functionA 5-minute orientation
- Skim a recent paper: Probability density function forecasting of residential electric vehicles charging profileInfluential work since 2022
- Pick up a classic book: Regional-scale hydrology with a new land surface processes modelThe most-reprinted book on the subject
- Read the landmark paper: On Estimation of a Probability Density Function and ModeCited 8,422 times
- Go sideways: Cumulative distribution functionA closely related topic
- Go sideways: Joint probability distributionA closely related topic
📖 Definitions
Noun Any function whose integral over a set gives the probability that a random variable has a value in that set.
🗂️ The subject at a glance
- Example
- Absolutely continuous univariate distributions
- Formal definition
- Further details
- Link between discrete and continuous distributions
- Families of densities
- Densities associated with multiple variables
- Function of random variables and change of variables in the probability density function
- Sums of independent random variables
- Products and quotients of independent random variables
🏆 Landmark papers (most cited)
On Estimation of a Probability Density Function and Mode
Probability Density Function Estimation Using Gamma Kernels
Experimental Lagrangian acceleration probability density function measurement
An introductory survey of probability density function control
Probability-density-function characterization of multipartite entanglement
Probability density function of turbulent velocity fluctuations
Model-based probability density function estimation
Probability density function estimation using the MinMax measure
🆕 Influential since 2022
Probability density function forecasting of residential electric vehicles charging profile
Time-dependent probability density function for partial resetting dynamics
Enhancing cosmic shear with the multiscale lensing probability density function
Radial basis function neural networks solution for stationary probability density function of nonlinear stochastic systems
A new probability density function for the surface elevation in irregular seas
📚 Books worth reading
- 📕Regional-scale hydrology with a new land surface processes modelCharles A. Laymon · 1995
- 📕A remote-sensing based technique to account for sub-grid scale variability of land surface propertiesWilliam L. Crosson · 1995
- 📕Statistical short-range guidance for peak wind speed forecasts on Kennedy Space Center/Cape Canaveral Air Force StationWinifred C. Lambert · 2002
- 📕Probability density functions of observed rainfall in MontanaScott D. Larsen · 1995
- 📕Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump deviceM. Simon · 1986
- 📕Nonstationary dynamics data analysis with wavelet-SVD filteringMarty Brenner · 2001
- 📕Mapping closure approximation to conditional dissipation rate for turbulent scalar mixingGouwei He · 2000
- 📕PDF methods for combustion in high-speed turbulent flowsStephen B. Pope · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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