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Types of Skewness

Types of Skewness

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,...

Skewness

Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency...

Divergence and Curl

Divergence and Curl

The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...

Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...

Gauss's Law: Cylindrical Symmetry

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...

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α-Geodesical Skew Divergence.

Masanari Kimura¹, Hideitsu Hino²

¹Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies (SOKENDAI), Kanagawa 240-0193, Japan.

Entropy (Basel, Switzerland)

|April 30, 2021

Summary

This summary is machine-generated.

This study introduces the α-geodesical skew divergence, a novel information geometric approach. This method generalizes skew divergence for improved distribution analysis without strict continuity requirements.

Keywords:

JS-divergence KL-divergence information geometry skew divergence

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Area of Science:

Information Theory
Probability and Statistics
Information Geometry

Background:

Skew divergence offers an approximation to KL divergence, relaxing absolute continuity constraints.
It involves smoothing one distribution by mixing it with another, controlled by parameter λ.

Purpose of the Study:

To propose and study the properties of an information geometric generalization of skew divergence.
Introduce the novel concept of α-geodesical skew divergence.

Main Methods:

Developing an information geometric framework for skew divergence.
Investigating the mathematical properties of the proposed α-geodesical skew divergence.

Main Results:

The α-geodesical skew divergence is formally defined and its theoretical properties are explored.
This generalization extends the applicability of skew divergence in information geometry.

Conclusions:

The proposed α-geodesical skew divergence provides a new tool in information geometry.
It offers a flexible approach for comparing probability distributions with relaxed continuity conditions.