Jove
Visualize
Contact Us

Related Concept Videos

Probability Distributions01:32

Probability Distributions

11.2K
 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...
11.2K
Poisson Probability Distribution01:09

Poisson Probability Distribution

11.2K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
11.2K
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.8K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
4.8K
Binomial Probability Distribution01:15

Binomial Probability Distribution

14.7K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
14.7K
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

3.4K
The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
3.4K
Probability Histograms01:17

Probability Histograms

12.9K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
12.9K

You might also read

Related Articles

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

Sort by
Same author

On the Accurate Estimation of Information-Theoretic Quantities from Multi-Dimensional Sample Data.

Entropy (Basel, Switzerland)·2024
Same author

Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples.

Entropy (Basel, Switzerland)·2021
See all related articles
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 Experiment Video

Updated: Nov 27, 2025

A Tactile Automated Passive-Finger Stimulator TAPS
19:44

A Tactile Automated Passive-Finger Stimulator TAPS

Published on: June 3, 2009

14.0K

A Maximum-Entropy Method to Estimate Discrete Distributions from Samples Ensuring Nonzero Probabilities.

Paul Darscheid1, Anneli Guthke2, Uwe Ehret1

  • 1Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology-KIT, 76131 Karlsruhe, Germany.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for constructing discrete probability distributions, ensuring all bins have a non-zero probability. The Clopper-Pearson method, along with "add one counter" and Bayesian approaches, performs best for estimating distributions, especially with small sample sizes.

Keywords:
Clopper–Pearsondiscrete distributionempty binhistogrammaximum entropy approachsamplezero probability

More Related Videos

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

34.2K
Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.4K

Related Experiment Videos

Last Updated: Nov 27, 2025

A Tactile Automated Passive-Finger Stimulator TAPS
19:44

A Tactile Automated Passive-Finger Stimulator TAPS

Published on: June 3, 2009

14.0K
Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

34.2K
Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

8.4K

Area of Science:

  • Statistics
  • Data Science
  • Probability Theory

Background:

  • Constructing discrete distributions from data samples often requires ensuring non-zero probability for all bins.
  • Existing methods like adding one counter, probability smoothing, and Bayesian approaches have limitations.
  • Accurate distribution estimation is crucial for predictive modeling and divergence measures like Kullback-Leibler.

Purpose of the Study:

  • To propose and evaluate a novel method for constructing discrete distributions with guaranteed non-zero bin probabilities.
  • To compare the performance of the proposed method against existing estimators using various distribution types.
  • To identify the most effective methods for distribution estimation, particularly for small sample sizes.

Main Methods:

  • Developed a new approach based on the Clopper-Pearson method utilizing the binomial distribution.
  • Calculated confidence intervals for bin-occupation probabilities to derive strictly positive estimators.
  • Compared the proposed method and four alternatives (add one counter, probability smoothing, Dirichlet-multinomial) using Kullback-Leibler divergence across diverse distributions.

Main Results:

  • The proposed Clopper-Pearson-based method effectively ensures non-zero bin probabilities and converges towards a uniform distribution for small samples, acting as a maximum entropy approach.
  • Performance varied by distribution type, but the proposed method, 'add one counter', and the Dirichlet-multinomial model consistently performed best on average.
  • These top-performing methods showed particularly strong results for small sample sizes.

Conclusions:

  • The Clopper-Pearson-based method is a favorable approach for estimating discrete distributions when the underlying shape is unknown.
  • For general distribution estimation without prior assumptions, the proposed method, 'add one counter', or the Bayesian Dirichlet-multinomial model are recommended.
  • These methods provide robust and accurate distribution estimates, especially crucial in scenarios with limited data.