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

Data: Types and Distribution01:19

Data: Types and Distribution

924
In biostatistics, data are the observations collected for analysis. There are two main types: parametric and non-parametric. Parametric data, which include continuous (e.g., weight) and discrete numerical data (e.g., number of tablets), assume a particular distribution pattern, often the normal distribution. Non-parametric data do not adhere to a specific distribution and typically comprise nominal (e.g., gender) and ordinal categorical data (e.g., pain scale ratings).
Distributions in...
924
Probability Distributions01:32

Probability Distributions

9.8K
 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...
9.8K
The Bell Curve01:21

The Bell Curve

444
The normal probability distribution, often depicted as a symmetrical, bell-shaped curve, is fundamental in statistics and the study of natural phenomena. This pattern, famously described by mathematician Carl Friedrich Gauss, shows how data points are distributed around a central mean, with most values near the average and fewer observations occurring as they deviate further from it.
This pattern applies to many human characteristics beyond intelligence, such as height. For example, if you...
444
Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

299
In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within...
299
Chi-square Distribution01:10

Chi-square Distribution

5.2K
How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people preferred were different across different age groups or if a coffee machine dispensed approximately the same amount of coffee each time. These questions can be addressed by conducting a hypothesis test. One distribution that can be used to find answers to such questions is known as the chi-square distribution. The chi-square distribution has...
5.2K
Types of Skewness01:09

Types of Skewness

14.2K
If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
14.2K

You might also read

Related Articles

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

Sort by
Same author

False discovery rate control for grouped hypotheses: application to miRNAome data.

PeerJ·2026
Same author

Dissecting the coordinated progression of cell states in spatial transcriptomics with CoPro.

bioRxiv : the preprint server for biology·2026
Same author

Rural and urban attitudes to conflict and cooperation with wildfowl conservation directives in a community in China.

Conservation biology : the journal of the Society for Conservation Biology·2026
Same author

Semi-Supervised Off-Policy Reinforcement Learning and Value Estimation for Dynamic Treatment Regimes.

Journal of machine learning research : JMLR·2026
Same author

Urban-Rural Differences in Preferences for Environmentally Friendly Farming from the Perspectives of Oriental White Stork Conservation.

Animals : an open access journal from MDPI·2026
Same author

Research on drug-drug interaction prediction using capsule neural network based on self-attention mechanism.

BMC bioinformatics·2025
Same journal

Comparing Adaptive Interventions under a General Sequential Multiple Assignment Randomized Trial Design via Multiple Comparisons with the Best.

Journal of statistical planning and inference·2026
Same journal

Variable Selection in Ultra-high Dimensional Feature Space for the Cox Model with Interval-Censored Data.

Journal of statistical planning and inference·2026
Same journal

On semi-supervised estimation using exponential tilt mixture models.

Journal of statistical planning and inference·2025
Same journal

Regression-Assisted Bayesian Record Linkage for Causal Inference in Observational Studies with Covariates Spread Over Two Files.

Journal of statistical planning and inference·2024
Same journal

Efficient inference of parent-of-origin effect using case-control mother-child genotype data.

Journal of statistical planning and inference·2024
Same journal

Distributed eQTL analysis with auxiliary information.

Journal of statistical planning and inference·2024
See all related articles

Related Experiment Video

Updated: Oct 18, 2025

How to Create and Use Binocular Rivalry
14:34

How to Create and Use Binocular Rivalry

Published on: November 10, 2010

75.9K

Bi-s*-Concave Distributions.

Nilanjana Laha1, Zhen Miao2, Jon A Wellner2

  • 1Department of Biostatistics, Harvard University, 677 Huntington Ave, Boston, MA 02115.

Journal of Statistical Planning and Inference
|October 4, 2021
PubMed
Summary
This summary is machine-generated.

We introduce novel bi-s*-concave distribution functions, a new class of shape-constrained functions. These functions generalize existing bi-log-concave distributions and enable improved confidence bands in statistical analysis.

Keywords:
Csörgő - Révész conditionbi-log-concavehazard functionlog-concavequantile processs-concaveshape constraint

More Related Videos

Precision Measurements and Parametric Models of Vertebral Endplates
10:35

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

6.7K
Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients
07:06

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients

Published on: March 29, 2022

2.8K

Related Experiment Videos

Last Updated: Oct 18, 2025

How to Create and Use Binocular Rivalry
14:34

How to Create and Use Binocular Rivalry

Published on: November 10, 2010

75.9K
Precision Measurements and Parametric Models of Vertebral Endplates
10:35

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

6.7K
Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients
07:06

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients

Published on: March 29, 2022

2.8K

Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Distribution functions are fundamental in statistical modeling.
  • Existing shape constraints like bi-log-concavity have limitations.
  • Nonparametric confidence bands are crucial for statistical inference.

Purpose of the Study:

  • Introduce new shape-constrained distribution functions: bi-s*-concave classes.
  • Extend existing results for bi-log-concave distributions.
  • Develop novel confidence bands that incorporate bi-s*-concavity.

Main Methods:

  • Define and analyze the properties of bi-s*-concave distribution functions.
  • Establish the relationship between s-concave densities and bi-s*-concave distribution functions.
  • Adapt and build upon existing nonparametric confidence bands.

Main Results:

  • Demonstrate that every s-concave density has a bi-s*-concave distribution function for s* ≤ s/(s + 1).
  • Introduce new confidence bands that account for bi-s*-concavity.
  • Show that the new bands extend those for bi-log-concavity.

Conclusions:

  • Bi-s*-concavity offers a valuable generalization for distribution functions.
  • The developed confidence bands provide enhanced statistical inference capabilities.
  • Connections are established with the Csörgő-Révész constant and quantile processes.