Moment (mathematics) | Statistical deviation and dispersion
In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Like skewness, kurtosis describes a particular aspect of a probability distribution. There are different ways to quantify kurtosis for a theoretical distribution, and there are corresponding ways of estimating it using a sample from a population. Different measures of kurtosis may have different . The standard measure of a distribution's kurtosis, originating with Karl Pearson, is a scaled version of the fourth moment of the distribution. This number is related to the tails of the distribution, not its peak; hence, the sometimes-seen characterization of kurtosis as "peakedness" is incorrect. For this measure, higher kurtosis corresponds to greater extremity of deviations (or outliers), and not the configuration of data near the mean. It is common to compare the excess kurtosis (defined below) of a distribution to 0, which is the excess kurtosis of any univariate normal distribution. Distributions with negative excess kurtosis are said to be platykurtic, although this does not imply the distribution is "flat-topped" as is sometimes stated. Rather, it means the distribution produces fewer and/or less extreme outliers than the normal distribution. An example of a platykurtic distribution is the uniform distribution, which does not produce outliers. Distributions with a positive excess kurtosis are said to be leptokurtic. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution. It is common practice to use excess kurtosis, which is defined as Pearson's kurtosis minus 3, to provide a simple comparison to the normal distribution. Some authors and software packages use "kurtosis" by itself to refer to the excess kurtosis. For clarity and generality, however, this article explicitly indicates where non-excess kurtosis is meant. Alternative measures of kurtosis are: the L-kurtosis, which is a scaled version of the fourth L-moment; measures based on four population or sample quantiles. These are analogous to the alternative measures of skewness that are not based on ordinary moments. (Wikipedia).
What is an angle and it's parts
👉 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
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From playlist Miscellaneous
👉 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
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
The Definition of a Linear Equation in Two Variables
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From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
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From playlist Differential Equations
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Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
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From playlist Philosophy of Science
Kurtosis of a probability distribution (FRM T2-7)
[Here is my xls http://trtl.bz/121817-yt-kurtosis-xls] Kurtosis is the standardized fourth central moment and is a measure of tail density; e.g., heavy or fat-tails. Heavy-tailedness also tends to correspond to high peakedness. Excess kurtosis (aka, leptokurtosis) is given by (kurtosis-3).
From playlist Quantitative Analysis (FRM Topic 2)
What is Kurtosis? (+ the "peakedness" controversy!)
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From playlist Descriptive Statistics (13 videos)
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I have been thinking about kurtosis all wrong. Kurtosis is a measure of the thickness or heaviness of the tails of a distribution. Like skewness, kurtosis describes the shape of a probability distribution. It is often mistakenly characterized as “peakedness” of a distribution; however, kur
From playlist Depicting Distributions from Boxplots to z-Scores (WK 6 QBA 237)
I illustrate how to manually calculate skew and kurtosis with Google's daily price data from 2007. The point is the variance, skew and kurtosis are each related MOMENTS of the distribution. A normal distribution has skew = 0 and kurtosis = 3 https://www.dropbox.com/s/9ge1gckgqhahcou/2.a.1
From playlist Statistics: Distributions
Moments are measures that tell us something about a distribution (e.g., does it have fat tails?). The first four moments are the following. Mean: a measure of central tendency (a.k.a., location). Variance: a measure of dispersion or scatter (a.k.a., scale). Skew: a measure of symmetry or
From playlist Statistics: Distributions
Skewness and Kurtosis : the two summary stats they never taught you
All about Skewness and Kurtosis, the two missing summary statistics they never taught you! My Patreon : https://www.patreon.com/user?u=49277905 0:00 Average 2:13 Standard Deviation 4:00 Skewness 6:53 Kurtosis
From playlist Data Science Basics
How to find Kurtosis Excel 2013
Visit us at http://www.statisticshowto.com for more videos and Excel tips.
From playlist Excel for Statistics
Checking normality using skewness, kurtosis, Kolmogorov–Smirnov and Shapiro-Wilk tests
In this video, I will explain how to use SPSS to evaluate check for normality using skewness, kurtosis, Kolmogorov–Smirnov and Shapiro-Wilk tests. Please also check the following video for further information: https://www.youtube.com/watch?v=Wql-YRAoX6I The criteria that I will explain
From playlist Descriptive Statistics SPSS
R - Basic Statistics (3.1 Flip)
Lecturer: Dr. Erin M. Buchanan Spring 2021 https://www.patreon.com/statisticsofdoom This video covers an introduction to basic statistical concepts such as frequency distributions, measures of central tendency, skew, kurtosis, variance, standard deviation, and z-scores. These videos a
From playlist Graduate Statistics Flipped
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👉 Learn how to solve problems with trapezoids. A trapezoid is a four-sided shape (quadrilateral) such that one pair of opposite sides are parallel. Some of the properties of trapezoids are: one pair of opposite sides are parallel, etc. A trapezoid is isosceles is one pair of opposite sides
From playlist Properties of Trapezoids
Normality check, skewness, and kurtosis in free software JASP with references
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From playlist Descriptive Statistics SPSS