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

Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

488
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...
488
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.1K
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...
4.1K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

99
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
99
Poisson Probability Distribution01:09

Poisson Probability Distribution

8.3K
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...
8.3K
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

2.8K
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...
2.8K
Normal Distribution01:11

Normal Distribution

11.5K
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...
11.5K

You might also read

Related Articles

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

Sort by
Same author

Scientific evidence validating spiritual beliefs for controlling pathogenic microbes in the Ganga river.

Journal of environmental sciences (China)·2026
Same author

An interactive machine learning platform for analyzing multi-particle coincidence data from cold target recoil ion momentum spectroscopy.

The Review of scientific instruments·2026
Same author

Chaos quasi-opposition arithmetic algorithm-based Robust improved frequency regulation for restructured hybrid power system integrating renewable energy sources.

Scientific reports·2026
Same author

Lifestyle Behavioral Self-Care Practices and Their Determinants Among Type 2 Diabetes Patients Attending a Non-communicable Disease Clinic in Agra District: A Cross-Sectional Study.

Cureus·2026
Same author

Unlocking Neuroprotection: Potassium Channel Openers in Alzheimer's Disease.

Current Alzheimer research·2026
Same author

Rice at risk: How double burden of climate change and arsenic threaten food security and human health in vulnerable nations.

The Science of the total environment·2025

Related Experiment Video

Updated: Jul 25, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

4.7K

Shifted Mixture Model Using Weibull, Lognormal, and Gamma Distributions.

Sarvesh Kumar1, Madhu Jain1

  • 1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 India.

National Academy Science Letters. National Academy of Sciences, India
|June 26, 2023
PubMed
Summary

This study introduces new mixture models using Weibull, lognormal, and gamma distributions. For small datasets, the shifted mixture model demonstrates superior performance in statistical and reliability analyses.

Keywords:
EM algorithm reliability indicesGoodness of fitMLEShifted mixture distribution

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
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

10.7K

Related Experiment Videos

Last Updated: Jul 25, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

4.7K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
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

10.7K

Area of Science:

  • Statistics
  • Reliability Engineering
  • Probability Distributions

Background:

  • Mixture models are widely used in various fields.
  • Existing models may not perform optimally for all data types.
  • Weibull, lognormal, and gamma distributions are common choices for modeling.

Purpose of the Study:

  • To develop a framework for constructing threefold mixture models and their shifted versions.
  • To evaluate the statistical and reliability properties of these proposed models.
  • To assess the performance of shifted mixture models on real-world data.

Main Methods:

  • Construction of threefold mixture models using Weibull, lognormal, and gamma distributions.
  • Parameter estimation via Maximum Likelihood Estimation (MLE) and Expectation-Maximization algorithms.
  • Application and comparison of models using goodness-of-fit tests on actual datasets.

Main Results:

  • The proposed mixture models and their shifted versions were successfully constructed.
  • Statistical and reliability indices were established for the models.
  • Shifted mixture models showed significant utility when fitted to real-life data.
  • Goodness-of-fit tests indicated the superiority of shifted models for certain datasets.

Conclusions:

  • The shifted mixture model, particularly for small datasets, is identified as the best-fitted model.
  • This research provides a valuable framework for applying advanced mixture models.
  • The findings have implications for data analysis in reliability and statistics.