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

Poisson Probability Distribution01:09

Poisson Probability Distribution

8.5K
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...
8.5K
Probability Distributions01:32

Probability Distributions

7.9K
 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...
7.9K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.5K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.5K
Binomial Probability Distribution01:15

Binomial Probability Distribution

11.4K
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,...
11.4K
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

628
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
628
Poisson's Ratio01:23

Poisson's Ratio

554
Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
554

You might also read

Related Articles

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

Sort by
Same author

An improved extension of Xgamma distribution: Its properties, estimation and application on failure time data.

Heliyon·2025
Same author

A new two-parameter over-dispersed discrete distribution with mathematical properties, estimation, regression model and applications.

Heliyon·2024
Same author

Modeling of COVID-19 Cases in Pakistan Using Lifetime Probability Distributions.

Annals of data science·2024
Same author

Classical and Bayesian inference for the new four-parameter Lomax distribution with applications.

Heliyon·2024
Same author

An exponentiated XLindley distribution with properties, inference and applications.

Heliyon·2024
Same author

Analysis of Covid-19 data using discrete Marshall-Olkinin Length Biased Exponential: Bayesian and frequentist approach.

Scientific reports·2023
Same journal

MT-MRI for detection of renal interstitial fibrosis in renovascular disease.

Scientific reports·2026
Same journal

Detection of underground objects from GPR data using a lightweight YOLO-based approach.

Scientific reports·2026
Same journal

Early systemic inflammatory-metabolic trajectory phenotypes are associated with survival outcomes in metastatic renal cell carcinoma treated with nivolumab.

Scientific reports·2026
Same journal

Water balance components in a dry-seeded rice-wheat system: Untangling the effects of tillage and mulching practices.

Scientific reports·2026
Same journal

Topological approaches to quantum tensor train compression via ZX-calculus and SVD.

Scientific reports·2026
Same journal

determinants of flood impacts and adaptive capacity among market vendors in Walukuba-Masese, Jinja city, Uganda.

Scientific reports·2026
See all related articles

Related Experiment Video

Updated: Sep 17, 2025

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

8.0K

Discrete Poisson Haq distribution with mathematical properties and count data modeling.

Abdullah M Alomair1, Faisal Ayyaz2, Saadia Tariq2

  • 1Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa, 31982, Saudi Arabia. ama.alomair@kfu.edu.sa.

Scientific Reports
|July 3, 2025
PubMed
Summary
This summary is machine-generated.

A new Poisson Haq (PH) distribution is introduced for analyzing over-dispersed count data. This flexible statistical model demonstrates superior performance compared to existing distributions in medical applications.

Keywords:
Discrete distributionEstimationHaq distributionMedical dataMixed Poisson

More Related Videos

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.5K

Related Experiment Videos

Last Updated: Sep 17, 2025

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

8.0K
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.5K

Area of Science:

  • Statistics
  • Probability Theory
  • Biostatistics

Background:

  • Count data often exhibit over-dispersion, violating assumptions of standard Poisson distributions.
  • Existing discrete distributions may not adequately capture the complexities of over-dispersed medical count data.
  • Need for flexible statistical models to analyze various biological and medical count datasets.

Purpose of the Study:

  • To propose a new one-parameter discrete distribution, the Poisson Haq (PH) distribution.
  • To analyze over-dispersed count datasets, particularly in medical contexts.
  • To develop and evaluate a parametric regression model based on the PH distribution.

Main Methods:

  • The Poisson Haq distribution is constructed as a mixture of Poisson and Haq random variables.
  • Statistical properties, including failure rate shapes (increasing and upside bathtub), are derived.
  • Parameter estimation is performed using the method of moments, maximum likelihood estimation, and Bayesian approaches with a gamma prior.

Main Results:

  • The PH distribution effectively models over-dispersed count data, showing improved fitting accuracy (lower AIC and BIC values) compared to Poisson, Poisson moment exponential, and Poisson-XLindley distributions.
  • Simulation studies confirm the performance and behavior of the proposed estimators.
  • The PH regression model demonstrates good fit for the Length of Hospital Stay dataset.

Conclusions:

  • The proposed Poisson Haq distribution offers a valuable and flexible alternative for analyzing over-dispersed count data in medical and biological research.
  • The PH distribution and its associated regression model provide enhanced accuracy and better data-fitting capabilities.
  • The model's applicability is validated across diverse medical datasets, including infectious diseases and cytogenetic lesions.