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Related Concept Videos

Pareto Chart00:52

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the lines represent the cumulative total values. In this chart, the longest bars are arranged on the left and the shortest bars on the right, which makes it easier to read and interpret the data. It can also be called a Pareto diagram or Pareto analysis.
The Pareto chart is named after the Italian economist Vilfredo Pareto, who described the Pareto...
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.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Poisson Probability Distribution01:09

Poisson Probability Distribution

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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Related Experiment Videos

[Origination of Pareto distribution in complex dynamic systems].

D S Chernavskiĭ, A P Nikitin, O D Chernavskaia

    Biofizika
    |June 12, 2008
    PubMed
    Summary

    The Pareto distribution, distinct from the Gaussian distribution, explains high deviations in dynamic systems. This study models its origin in Gaussian noise fields, showing precise approximation of system responses.

    Area of Science:

    • Statistical Physics
    • Probability Theory

    Context:

    • The widespread assumption of the Gaussian distribution's universal applicability lacks empirical support in many fields.
    • Dynamic systems influenced by Gaussian noise exhibit behaviors not captured by the normal distribution.

    Purpose:

    • To investigate the origins of the Pareto distribution within dynamic systems subjected to Gaussian noise.
    • To analyze a simplified one-dimensional model for approximating system responses.

    Summary:

    • The Pareto distribution, characterized by rho(chi) ~ chi(-alpha) for large chi (alpha >= 2), is theoretically and practically significant due to its higher probability of extreme deviations compared to the Gaussian distribution.
    • A one-dimensional dynamic system model exposed to Gaussian noise demonstrates that system responses can be accurately approximated by the Pareto distribution over a broad range.

    Related Experiment Videos

    Impact:

    • Challenges the overreliance on Gaussian models in scientific and practical applications.
    • Provides a theoretical framework and model for understanding phenomena exhibiting Pareto-like distributions, particularly in noisy environments.