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Related Concept Videos

Probability Distributions01:32

Probability Distributions

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.
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While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Distribution and Dispersion00:54

Distribution and Dispersion

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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Published on: February 9, 2017

The linear stochastic order and directed inference for multivariate ordered distributions.

Ori Davidov1, Shyamal Peddada

  • 1Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905 Israel.

Annals of Statistics
|April 2, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces linear stochastic order for comparing two experimental groups using multivariate data. The new method estimates separation direction and tests for order, generalizing existing statistical tests for broader applications.

Keywords:
nonparametric testsorder restricted statistical inferencestochastic order relations

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Area of Science:

  • Statistics
  • Biostatistics
  • Multivariate Analysis

Background:

  • Standard multivariate methods are often two-sided, limiting their use for ordered group comparisons.
  • Testing for order between experimental groups requires specialized statistical approaches.

Purpose of the Study:

  • Introduce and investigate the properties of the linear stochastic order.
  • Develop statistical methods to estimate the optimal separation direction between ordered distributions.
  • Test for order between two experimental groups using multivariate data.

Main Methods:

  • Developed the concept of linear stochastic order.
  • Created statistical theory and methodology for estimating separation direction.
  • Generalized Roy's largest root test to a nonparametric setting.
  • Methodology is applicable to discrete and/or continuous random vectors.

Main Results:

  • The proposed methodology effectively estimates the direction that best separates two ordered distributions.
  • Statistical tests for order between groups were developed and validated.
  • The approach generalizes existing methods to a nonparametric context.

Conclusions:

  • Linear stochastic order provides a powerful tool for analyzing ordered data in multivariate settings.
  • The developed methodology offers a flexible and robust approach for hypothesis testing in comparative studies.
  • The method is applicable to diverse data types and demonstrated with real-world bioassay data.