Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Uniform Distribution01:19

Uniform Distribution

The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.Two essential properties of this distribution are The area under the rectangular shape equals 1. There is a correspondence between the probability of an event and the area under the curve.Further, the mean and standard deviation of the uniform distribution can be calculated when the lower and upper cut-offs, denoted as a and b,...
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Normal Distribution01:11

Normal Distribution

The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is extremely...
Introduction to Normal Distributions01:29

Introduction to Normal Distributions

Standardized test scores often follow a symmetric distribution that can be modeled with the normal distribution, a fundamental concept in statistics. This distribution is particularly useful for interpreting test performance fairly across populations, as it provides a mathematical framework for understanding variability and central tendency in large datasets.From Histogram to Frequency DistributionRaw test data are often displayed using histograms, where the height of each bar represents the...
Chi-square Distribution01:10

Chi-square Distribution

How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people preferred were different across different age groups or if a coffee machine dispensed approximately the same amount of coffee each time. These questions can be addressed by conducting a hypothesis test. One distribution that can be used to find answers to such questions is known as the chi-square distribution. The chi-square distribution has...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Super-radiance reveals infinite-range dipole interactions through a nanofiber.

Nature communications·2017
Same author

Simulation and analysis of light scattering by multilamellar bodies present in the human eye.

Biomedical optics express·2017
Same author

Starlet transform applied to digital Gabor holographic microscopy.

Applied optics·2016
Same author

Phase mask coded with the superposition of four Zernike polynomials for extending the depth of field in an imaging system.

Applied optics·2014
Same author

Dynamic holographic gratings with photoresist.

Applied optics·2010
Same author

Computer holographic lens.

Applied optics·2010
Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026
Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026
Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026
Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026
Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026
Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026
See all related articles

Related Experiment Video

Updated: Jul 3, 2026

Analysis and Specification of Starch Granule Size Distributions
08:46

Analysis and Specification of Starch Granule Size Distributions

Published on: March 4, 2021

Unifying distribution functions: some lesser known distributions.

J R Moya-Cessa1, H Moya-Cessa, L R Berriel-Valdos

  • 1Centro de Investigaciones en Optica, A.C., Apartado Postal 1-948, León, Gto., Mexico.

Applied Optics
|August 2, 2008
PubMed
Summary
This summary is machine-generated.

This study presents a unified method for describing classical and quantum systems using distribution functions. It demonstrates how various functions, including the Wigner distribution, can be derived from operator ordering and expectation values.

More Related Videos

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Related Experiment Videos

Last Updated: Jul 3, 2026

Analysis and Specification of Starch Granule Size Distributions
08:46

Analysis and Specification of Starch Granule Size Distributions

Published on: March 4, 2021

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

  • Quantum mechanics
  • Signal processing
  • Mathematical physics

Background:

  • Distribution functions are crucial for describing classical and quantum systems.
  • The Wigner distribution function is a well-known example used in quantum mechanics.
  • Existing functions like Cohen's class, Rihaczek's, Husimi's, and Glauber-Sudarshan's have distinct applications.

Purpose of the Study:

  • To develop a unified framework for distribution functions.
  • To demonstrate a method for unifying classical and quantum descriptions.
  • To connect various existing distribution functions within a single theoretical structure.

Main Methods:

  • Utilizing ordered forms of creation and annihilation operators.
  • Deriving distribution functions from expectation values in different eigenbases.
  • Applying a unified approach to functions within Cohen's class and other named distributions.

Main Results:

  • A method to unify diverse distribution functions has been established.
  • The study shows how these functions can be obtained from operator ordering.
  • Expectation values in different eigenbases provide a route to these unified functions.

Conclusions:

  • A generalized approach to distribution functions offers a more comprehensive understanding.
  • This unification simplifies the theoretical landscape of signal and quantum state description.
  • The findings provide a pathway to explore new theoretical and practical applications.