The Theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation. The Theil index TT is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. It is a special case of the generalized entropy index. It can be viewed as a measure of redundancy, lack of diversity, isolation, segregation, inequality, non-randomness, and compressibility. It was proposed by a Dutch econometrician Henri Theil (1924-2000) at the Erasmus University Rotterdam. Henri Theil himself said (1967): "The (Theil) index can be interpreted as the expected information content of the indirect message which transforms the population shares as prior probabilities into the income shares as posterior probabilities." Amartya Sen noted, "But the fact remains that the Theil index is an arbitrary formula, and the average of the logarithms of the reciprocals of income shares weighted by income is not a measure that is exactly overflowing with intuitive sense." (Wikipedia).
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
Identify the Level of Measurement MyMathlab Statistics Homework
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From playlist Statistics
Vernier caliper / diameter and length of daily used objects.
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From playlist Fine Measurements
Statistics 3 Measures of Central Tendency.mov
Discussing measures of central tendency, such as mean or average, median, and mode.
From playlist Medical Statistics
From playlist Basic Statistics (Descriptive Statistics)
Statistics 5_1 Confidence Intervals
In this lecture explain the meaning of a confidence interval and look at the equation to calculate it.
From playlist Medical Statistics
Determining values of a variable at a particular percentile in a normal distribution
From playlist Unit 2: Normal Distributions
Statistics Lecture 3.3: Finding the Standard Deviation of a Data Set
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From playlist Statistics (Full Length Videos)
Not quite a quasicrystal (yet): Particles interacting with a potential based on the golden ratio
This new attempt at growing a quasicrystal uses a potential with rotation symmetry, which is similar to the Lennard-Jones potential, but has two stable equilibrium positions at distances whose ratio ls the golden mean Phi = 1.618.... This was suggested to me by Florian Theil. The result is
From playlist Molecular dynamics
Levels of Measurement MyMathlab Statistics Example with Bad Calculation
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From playlist Statistics
Freezing and melting at the molecular scale: a representation with atomic bonds
This is a variant of the simulation https://youtu.be/z6duw2xm53c with similar parameter values, but a different graphical representation: particles are connected by lines to their neighbors within a fixed distance, to make the crystalline structures more visible. Thanks to Florian Theil fo
From playlist Molecular dynamics
Inserting an atom in a crystal
This #short simulation shows particles interacting with a Lennard-Jones potential coupled to a thermostat. At the beginning of the simulation, the particles are close to equilibrium in a triangular lattice. 12 seconds after the beginning of the simulation, a new particle is inserted at a r
From playlist Molecular dynamics
Interacting particles with spins
This simulation is a first step towards systems of interacting particles that have a rotational degree of freedom. Here each particle carries an angle, or "spin", indicated by a little dash. The particles interact with a Lennard-Jones potential, which determines the evolution of their posi
From playlist Molecular dynamics
An hourglass with Lennard-Jones particles
This #short simulation shows 199 particles interacting with a Lennard-Jones potential, coupled to a thermostat, and confined to a region shaped like an hour glass. The particles' color indicates their kinetic energy: red particles move faster than blue ones. The motion can also be a fast o
From playlist Molecular dynamics
Deep impact: Throwing large discs into a Lennard-Jones crystal
In this simulation, five massive discs of decreasing size are thrown into a "sea" containing 2079 small particles interacting with a Lennard-Jones potential. I had in mind producing some kind of impact crater surrounded by ejecta, but it turns out that the particles are too mobile for the
From playlist Molecular dynamics
Under pressure: Particles with Lennard-Jones interaction in a piston
One nice feature of molecular dynamics is that it allows to illustrate all kinds of physical phenomena. In this simulation, 869 particles are kept in a container into which a piston is slowly pushed, thereby reducing the available volume. This forces the particles to arrange in a more and
From playlist Molecular dynamics
This simulation illustrates the phenomenon of osmosis, and is inspired by the nice video https://youtu.be/2OOvMiKCp8A by Eugene Khutoryansky@Physics Videos by Eugene Khutoryansky , that a commenter pointed out to me. There are 346 particles of two different types, interacting with a Lennar
From playlist Molecular dynamics
In step polymerization, polymers of any size can merge to form larger polymers. This simulation starts with 2277 elementary molecules (monomers), shown in red. These can merge to form dimers (in yellow), and larger polymers, of size up to 9, shown in various shades of green and blue. Polym
From playlist Molecular dynamics
Evaporation/sublimation of a Lennard-Jones crystal under heating and gravity
This video is a first attempt at illustrating what happens when a solid or liquid evaporates when heated. It shows 863 particles interacting via a Lennard-Jones potential, subjected to gravity, confined to a rectangular domain by a stiff harmonic potential, and coupled to a thermostat with
From playlist Molecular dynamics
Determine if the Given Value is from a Discrete or Continuous Data Set MyMathlab Statistics
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From playlist Statistics