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

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
Distribution and Dispersion00:54

Distribution and Dispersion

22.4K
To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
22.4K
Uniform Distribution01:19

Uniform Distribution

5.2K
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
5.2K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.7K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.7K
Random Error01:04

Random Error

1.6K
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
1.6K
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

You might also read

Related Articles

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

Sort by
Same author

Determinants of BCG vaccine coverage among 0-2 months aged Somali children: Promoting equality in vaccination.

Human vaccines & immunotherapeutics·2026
Same author

Socio-digital stratification and the threshold effects of digital inclusion on maternal health access in Somalia.

Global health action·2026
Same author

A novel adaptive quasi-Newton-type update and its global convergence without Lipschitz condition for constrained system of nonlinear monotone equations.

PloS one·2026
Same author

Simulation based new method for population variance using auxiliary information.

Scientific reports·2026
Same author

Patterns of Intensive Care Unit Mortality from Natural Causes at a Tertiary Care Centre in Western Nepal: An Observational Study.

JNMA; journal of the Nepal Medical Association·2026
Same author

Determinants of women's autonomy in healthcare decision-making in Somalia: evidence from the 2020 demographic and health survey.

International journal for equity in health·2026

Related Experiment Video

Updated: Sep 12, 2025

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.4K

Inverse unit compound Rayleigh distribution: statistical properties with applications in different fields.

Hatem E Semary1, Emmanuel W Okereke2, Laxmi Prasad Sapkota3

  • 1Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia.

Scientific Reports
|August 8, 2025
PubMed
Summary

A new inverse unit compound Rayleigh distribution (IUCRD) is introduced, offering flexible properties and demonstrating superior performance in real-world data analysis compared to existing distributions.

Keywords:
Estimation methodsHeavy-tailed distributionSimulationUnimodal distributionUnit compound Rayleigh distribution

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

8.0K
Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

10.4K

Related Experiment Videos

Last Updated: Sep 12, 2025

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.4K
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
Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

10.4K

Area of Science:

  • Statistics
  • Probability Distributions
  • Mathematical Modeling

Background:

  • The need for flexible probability distributions in statistical modeling is ongoing.
  • Existing distributions may not adequately capture the complexities of all real-world data.
  • The unit compound Rayleigh distribution (UCRD) serves as a basis for developing new distributions.

Purpose of the Study:

  • To introduce and characterize a novel two-parameter distribution: the inverse unit compound Rayleigh distribution (IUCRD).
  • To explore the mathematical properties of the IUCRD, including its quantile function, mode, moments, and heavy-tailedness.
  • To evaluate the performance of the IUCRD against existing distributions using real-world datasets.

Main Methods:

  • The IUCRD is derived via the inverse transformation of the UCRD.
  • Key statistical properties of the IUCRD are mathematically derived and analyzed.
  • Parameter estimation methods, including KE and ML, are compared using Monte Carlo simulations.
  • Goodness of fit statistics are employed to compare the IUCRD with other distributions on real-world data.

Main Results:

  • The IUCRD exhibits flexible properties, including unimodal or non-increasing PDF, and adjustable skewness.
  • The hazard rate function of the IUCRD can be upside-down bathtub-shaped or non-decreasing.
  • The KE method is identified as the best estimation methodology, with ML as the second best.
  • The IUCRD demonstrates superior fit to five real-world datasets compared to seven other distributions.

Conclusions:

  • The inverse unit compound Rayleigh distribution (IUCRD) is a valuable addition to the family of continuous probability distributions.
  • The IUCRD's flexibility and demonstrated superior fit make it a preferable choice for various data analysis scenarios.
  • The study validates the utility of the IUCRD in practical applications, outperforming established distributions like UCRD and inverse exponential variants.