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Related Concept Videos

Poisson Probability Distribution01:09

Poisson Probability Distribution

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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...
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Poisson's And Laplace's Equation01:25

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The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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Poisson's Ratio01:23

Poisson's Ratio

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Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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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...
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Residuals and Least-Squares Property01:11

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Modified ridge-type for the Poisson regression model: simulation and application.

Adewale F Lukman1, Benedicta Aladeitan1, Kayode Ayinde2

  • 1Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel estimator for Poisson regression models facing multicollinearity. The new method demonstrates superior performance over existing techniques in simulations and real-world data analysis.

Keywords:
Liu estimatorPoisson maximum likelihood estimatorPoisson regression modelPoisson ridge regressionmulticollinearitysimulation

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Poisson regression models (PRM) analyze count data relationships.
  • Multicollinearity inflates variance of Poisson maximum likelihood estimator (PMLE).
  • Existing alternatives include Poisson ridge regression (PRRE) and Liu estimator (PLE).

Purpose of the Study:

  • Propose a new estimator for PRM coefficients under multicollinearity.
  • Evaluate the proposed estimator against existing methods.

Main Methods:

  • Developed a novel estimator for PRM.
  • Conducted simulation studies with varying specifications.
  • Applied estimators to aircraft damage data.

Main Results:

  • The proposed estimator showed better performance theoretically.
  • Simulation results supported the superiority of the new estimator.
  • Application to aircraft damage data confirmed improved performance.

Conclusions:

  • The new estimator effectively addresses multicollinearity in PRM.
  • The proposed method offers an improved alternative to PMLE, PRRE, and PLE.