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

Confidence Intervals01:21

Confidence Intervals

6.7K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
6.7K
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
Central Limit Theorem01:14

Central Limit Theorem

15.4K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
15.4K
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

4.5K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
4.5K
Uniform Distribution01:19

Uniform Distribution

5.1K
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
5.1K
Prediction Intervals01:03

Prediction Intervals

2.3K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.3K

You might also read

Related Articles

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

Sort by
Same author

Complex Effects of Salt on Small-Angle X-ray Scattering of BSA Originate from the Interplay of Ions and Hydration Water.

The journal of physical chemistry letters·2026
Same author

Counteraction of HMGB1 at ss-dsDNA junctions maintains liquidity of protamine-DNA co-condensates.

bioRxiv : the preprint server for biology·2026
Same author

A membrane insertion code for intrinsically disordered proteins.

bioRxiv : the preprint server for biology·2026
Same author

Measuring bridging forces in protein-DNA condensates.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

DIRseq as a method for predicting drug-interacting residues of intrinsically disordered proteins from sequences.

eLife·2025
Same author

Correlated Segments of Intrinsically Disordered Proteins as Drivers of Homotypic Phase Separation.

JACS Au·2025

Related Experiment Video

Updated: Jul 30, 2025

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.0K

Power law in a bounded range: Estimating the lower and upper bounds from sample data.

Huan-Xiang Zhou1

  • 1Department of Chemistry and Department of Physics, University of Illinois Chicago, Chicago, Illinois 60607, USA.

The Journal of Chemical Physics
|May 15, 2023
PubMed
Summary

Estimating bounds for power law distributions is challenging. This study introduces a new O(N) method using sample means to accurately determine lower and upper bounds, improving efficiency for analyzing scientific data.

More Related Videos

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

7.5K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.6K

Related Experiment Videos

Last Updated: Jul 30, 2025

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.0K
Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

7.5K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.6K

Area of Science:

  • Physics
  • Geophysics
  • Biology
  • Chemistry

Background:

  • Power law distributions are prevalent across various scientific disciplines.
  • Estimating the lower and upper bounds of these distributions from sample data is a significant challenge.
  • Existing methods for bound estimation can be computationally intensive, requiring O(N^3) operations.

Purpose of the Study:

  • To develop a computationally efficient method for estimating the lower and upper bounds of power law distributions.
  • To provide an alternative to existing O(N^3) methods with an O(N) approach.
  • To enhance the analysis of data exhibiting power law characteristics.

Main Methods:

  • The proposed approach involves calculating the mean values of the minimum (x̂min) and maximum (x̂max) values from N-point samples.
  • Estimates for the lower and upper bounds are derived by fitting x̂min or x̂max as a function of sample size N.
  • This method reduces computational complexity to O(N) operations.

Main Results:

  • The developed O(N) method accurately estimates both lower and upper bounds of power law distributions.
  • Validation using synthetic data confirmed the approach's reliability and precision.
  • The new method offers a significant improvement in computational efficiency compared to previous techniques.

Conclusions:

  • This O(N) method provides an efficient and reliable tool for estimating bounds in power law distributions.
  • The approach has broad applicability in fields where power law phenomena are studied.
  • Accurate bound estimation is crucial for the correct interpretation of power law data in science.