Lorenz asymmetry coefficient

Summary statistics

The Lorenz asymmetry coefficient (LAC) is a summary statistic of the Lorenz curve that measures the degree of asymmetry of the curve. The Lorenz curve is used to describe the inequality in the distribution of a quantity (usually income or wealth in economics, or size or reproductive output in ecology). The most common summary statistic for the Lorenz curve is the Gini coefficient, which is an overall measure of inequality within the population. The Lorenz asymmetry coefficient can be a useful supplement to the Gini coefficient. The Lorenz asymmetry coefficient is defined as where the functions F and L are defined as for the Lorenz curve, and μ is the mean. If S > 1, then the point where the Lorenz curve is parallel with the line of equality is above the axis of symmetry. Correspondingly, if S < 1, then the point where the Lorenz curve is parallel to the line of equality is below the axis of symmetry. If data arise from the log-normal distribution, then S = 1, i.e., the Lorenz curve is symmetric. The sample statistic S can be calculated from n ordered size data, , using the following equations: , where m is the number of individuals with a size or wealth less than μ and . However, if one or more of the data size is equal to μ, then S has to defined as an interval instead of a number (see ). The Lorenz asymmetry coefficient characterizes an important aspect of the shape of a Lorenz curve. It tells which size or wealth classes contribute most to the population’s total inequality, as measured by the Gini coefficient. If the LAC is less than 1, the inequality is primarily due to the relatively many small or poor individuals. If the LAC is greater than 1, the inequality is primarily due to the few largest or wealthiest individuals. For incomes distributed according to a log-normal distribution, the LAC is identically 1. (Wikipedia).

Symmetry in Physics | Noether's theorem

▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on

From playlist Symmetry

What is the Lorentz Transformation?

What is the Lorentz Transformation? It is a tool we use to relate the different experiences of different observers in special relativity. It is also one of the defining features of special relativity and what differentiates it from Galilean relativity. In this video, we will derive the Lor

From playlist Relativity

Orthogonality and Orthonormality

We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one

From playlist Mathematics (All Of It)

Lorentz Transformations VS Galilean Transformations | Special Relativity

The goal of this video is to show that for small velocities, the Lorentz transformations are equivalent to the Galilean transformations. 00:00 Introduction 00:12 Galilean Transformation 00:46 Lorentz Transformations 01:09 Making a Connection 01:17 Mathematical Details References: [1] Ca

From playlist Special Relativity, General Relativity

What are adjacent angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

The Golden Ratio

This video introduces the Golden ratio and provides several examples of where the Golden ratio appears. http:mathispower4u.com

From playlist Mathematics General Interest

What is a linear pair

From playlist Angle Relationships

What is an angle and it's parts

From playlist Angle Relationships

Lorentz Covariance VS Lorentz Invariance: What's the Difference? | Special Relativity

In special relativity, Lorentz covariance and Lorentz invariance are two very important concepts. But what exactly are these concepts? In this video, we will find out! Contents: 00:00 Definitions 00:51 Examples If you want to help us get rid of ads on YouTube, you can support us on Patr

From playlist Special Relativity, General Relativity

Lorenz Curves and the Gini Coefficient

techniques for assessing and visualising the degree of income inequality in an economy

From playlist Micro Unit 6: Market Failure and the Government

06 Data Analytics: Spatial Heterogeneity

Lecture on measures of heterogeneity.

From playlist Data Analytics and Geostatistics

Mar. 16, Chapter 43 (The Klein-Gordon equation and scalar quantum fields)

From playlist Spring 2021 Course

Deep Learning of Dynamics and Coordinates with SINDy Autoencoders

This video by Kathleen Champion describes a new approach for simultaneously discovering models and an effective coordinate system using a custom SINDy autoencoder. Paper at PNAS: https://www.pnas.org/content/116/45/22445.abstract Kathleen Champion, Bethany Lusch, J. Nathan Kutz, Steven L

From playlist Research Abstracts from Brunton Lab

PySINDy tutorial 5: Building in physical priors with constraints

PySINDy (https://github.com/dynamicslab/pysindy) is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this tutorial video, we show how users can input physical constraints, conservation laws

From playlist Research Abstracts from Brunton Lab

PySINDy tutorial 2: Choosing algorithm hyperparameters

PySINDy (https://github.com/dynamicslab/pysindy) is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this tutorial video, we show how you can use PySINDy to tune hyperparameters such as the

From playlist Research Abstracts from Brunton Lab

Promoting global stability in data-driven models of quadratic nonlinear dynamics - Trapping SINDy

System identification methods attempt to discover physical models directly from a dataset of measurements, but often there are no guarantees that the resulting models are stable. This video abstract summarizes our recent work that builds in a notion of long-term boundedness (or global stab

From playlist Research Abstracts from Brunton Lab

MAE5790-16 waterwheel equations and Lorenz equations

Analysis of the waterwheel equations. Lorenz equations. Simple properties of the Lorenz system. Volume contraction. Fixed points and their linear stability. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 9.1, 9.2.

From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

Linear model for chaotic Lorenz system [HAVOK]

In this short video, we describe how the chaotic Lorenz system may be modeled with a sparse, integer-valued, skew-symmetric, linear system. This is based on the new Hankel Alternative View of Koopman (HAVOK) analysis. Read more about this work: Chaos as an Intermittently Forced Linea

From playlist Research Abstracts from Brunton Lab

What are adjacent angles and linear pairs

From playlist Angle Relationships

MAE5790-25 Using chaos to send secret messages

Lou Pecora and Tom Carroll's work on synchronized chaos. Proof of synchronization by He and Vaidya, using a Liapunov function. Kevin Cuomo and Alan Oppenheim's approach to sending secret messages with chaos. Secure versus private communications. Anecdotes about Princess Diana, the early da

From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

Lorenz asymmetry coefficient

Related pages