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Questions tagged [kurtosis]

a normalized fourth moment of a distribution or dataset.

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Partial skewness (kurtosis)

On Wikipedia one can read: In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random ...
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Unbiased Estimator of the Error Third and Fourth Central Moment in Regression Analysis

In linear regression an unbiased estimator of the error ($\epsilon$) variance is given by: $$MS = \dfrac{1}{n-p-1}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}$$ which is the sum of squares of ...
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Kurtosis risk interpretation

There is a True or False item that is confusing me a little bit. Statement says: "Kurtosis risk (also known as 'fat tails' risk) explicitly describes the situation of having more observations at ...
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Repeated Measures 2 Way Anova with non-normal non-balanced dataset

I'm doing an experiment where I test participants of two groups (experts/non-experts) under two conditions (eyes opened/eyes closed). From these tests I got 11 variables I want to compare between ...
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Does the peak of a Normal Distribution mean anything? [closed]

What does the peak of a Normal distribution show? Let's say if I have a flat peak, does this mean I have a larger variance? What if I have a sharp peak? For example, Does the "blue distribution" ...
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Violating the assumptions of one sample t-test and wilcoxon's sign test

As far as the background of my research is concerned, I developed a framework for sustainability management in organizations through a systematic review of literature and sustainability reports. That ...
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Error of Bias-Corrected Kurtosis Estimators

Background I've found two different bias-corrected estimators for the kurtosis. The first one is used in various software packages, such as MATLAB, and is called bias-corrected in the respective ...
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Can two different distributions have the same value of mean, variance, skewness, and kurtosis?

Assuming that you have two discrete population distributions. Can they have identical values of mean ,variance, skewness and kurtosis while being different in shape visually ? Do these four values ...
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Skewness and Kurtosis estimation methods [closed]

In finance time series literature ARCH and GARCH models are used to get an estimate of volatility. Are there similar models to estimate skewness and kurtosis?
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How do you find shape parameters of a Johnson distribution from skew and kurtosis?

I'm trying to generate random numbers from a distribution with given moments, in my field the Johnson family of distributions is typically used but I can't find anywhere how to set it's shape ...
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Is there any non-gaussian distribution has skewness 0 and kurtosis 3?

Is there any non-gaussian distribution has skewness $0$ and kurtosis $3$? Thanks!
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Density chart of S&P500

I am examining the daily log returns of the S&P500 Index and I have negative skewness and excess kurtosis. However when I chart the density plot I am seeing positive skewness - does this seem ...
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Application of Skewness and Kurtosis

Often in finance, stock prices are considered to follow a lognormal distribution while stock returns are considered to follow a normal distribution -prices are positive while returns can be negative(...
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Paired t-test of a non-normal data with sample size 66

I have a paired data with n=66. I understand that normality condition of differences data should be met to conduct a paired t-test. However, from the histogram, it doesn't appear so normal. The p-...
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$P(\lvert X - \mu\rvert \geq \sigma)$ as a measure of tailedness

I know that one of the standard measures for the "tailedness" of a distribution is kurtosis, i.e. fourth standardized central moment $\frac{\mu_4}{\sigma^4}$. This measure is sort of intuitive to me: ...
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Why does Uniform Distributions have no outliers?

I was reading about the relation between Kurtosis and Outliers on Wiki and got across a line 'An example of a platykurtic distribution is the uniform distribution, which does not produce outliers' [...
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Activation function for response distribution with high kurtosis/skew

When using neural network for regression problems, the standard approach is to use tanh for hidden layer activation and linear or tanh for output layer activation. The tanh function returns (-1, 1) ...
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How shape parameters are connected with mean, variance, skewness and kurtosis of generalized gamma distribution

I am writing a code in python that can generate probability distribution with given mean (m), variance (v), skewness (s) and kurtosis (k). In scipy library of python, there is a function named ...
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How to compute the normalized Mardia kurtosis?

Although the univariate kurtosis is a normalized number, I have come to understand that Mardia's multivariate kurtosis is not. Would someone be so kind to explain how I can normalize this statistic or ...
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Is a kurtosis of 1 unique to a equiprobable two-point distribution?

This question came up while having a look for a CLT for the sample variance which I found under this link (Theorem 5.3.2) from another stackexchange question which I can't remember. The Theorem from ...
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Why does kurtosis of residuals vs. standardized residuals differ in GARCH models?

So I have used GARCH modelling and obtained both residuals and standardized residuals from that model but kurtosis of both of this series should be same? I am using ...
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rule for Normality skewness $<|2.0|$ , kurtosis $<|9.0|$?

Quoting: As can be seen in Table 1, the experimental and control group distribution were sufficiently normal for the purpose of conducting a $t$-test (skewness $<|2.0|$ , kurtosis $<|9.0|...
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How to derive Bernoulli kurtosis

Can some one show me the steps to derive kurtosis of Bernoulli distribution? First $$E[X^i]=p \mathrm{\;\;\;for\;all\;}i$$ $$\begin{align}E[x-u/s]^4=&(EX^4-4uEX^3+6u^2EX^2-4u^3EX-u^4)/s^4 \\ ...
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Compare central distribution between two data sets

I have a distribution of empirical data (plotted in yellow) that I am comparing to simulated data (plotted in blue). I am interested in whether my empirical data (yellow) "clusters" around the ...
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Interpret if residuals are “close enough” to a normal distribution

I'm working in Python with statsmodels. I estimate a multiple regression model (n=10763; 12 predictors; r^2=0.216; all coefficients have signs pointing the correct direction and are significant). Then ...
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Measuring oscillation erratically or wave peridods

I am trying to use a statistic that shows how erratic one of my parameters is acting. We can see this graphically: Originally I attempted to find the sum of the absolute difference between each point ...
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Correlation coefficient with standard deviation

I quite often find myself testing hypotheses in which the standard deviation of one (Normally distributed) variable is linked to (the mean of) another variable. I would like to be able to express the ...
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Distinguish between underlying Distribution and data shape in data transforming?

My question is not well worded, which is part of the problem. I’m specifically trying to apply this to my understanding of Six Sigma, but it probably applies everywhere. I know that having a normal ...
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Finding kurtosis of signal

I have a signal (Y) with 200000 samples. I plotted probability density function (PDF) of the ...
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293 views

Dealing with excess kurtosis via GLM in R

I am working in R with a dataset that produces an error distribution under OLS with minimal skew, but excess kurtosis around 2. After researching the problem on Google for a day I've sorted out that ...
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Relationship between kurtosis and the center of a distribution

Some have stated that kurtosis is the "movement of probability mass from the “shoulders” of a distribution into its center and tails" where "center" is defined as the range between $\mu \pm\sigma$. I ...
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Is there such a thing as a trimmed skewness estimator?

I was wondering whether there is some equivalent of trimmed mean when estimating skewness (or kurtosis)? I am looking for something which would be called maybe a trimmed sample skewness or kurtosis. ...
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What is the correct way to add and subtract skewness from a distribution?

If I recall correctly, we can add and subtract variance if variables are independent, and have a mean of 0. I have two distributions that are summed up: (a) one with high variance, low skewness and ...
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Transformations to approximate normality with high kurtosis data

At my job I am working on standardizing some data. Right now we are simply using z-scores and it's causing some problems. For instance, one outlier has had three four or five standard deviation moves ...
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what is the asymptotic distribution of kurtosis?

i am going to do a Monet Carlo simulation to calculate the p value of kurtosis test statistic. For that i need the asymptotic distribution. I know that is normal distribution. But i dont know the ...
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Can you calculate probability with mean, SD, skewness, and kurtosis [duplicate]

I know that a standard normal distribution has mean 0, sd=1, skewness=0, and kurtosis=0. I can then transform a value and calculate which percentile it sits. 1.96 is in the top 97.5% Can I perform a ...
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Testing equality of higher moments (e.g., kurtosis)

I have two large samples which I expected to both be approximately normal, yet one has much greater excess kurtosis. Is there a way to test the likelihood of observing such a difference in kurtosis (i....
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Finding Pareto distribution's Kurtosis

I have no clue how to solve this question: Questions: Given that each of a,b,c,d and e is a digit from {0,1,2,3,...,9} and f is an alphabet from {A,B,C,D,...,Z} X has a Pareto distribution with ...
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inferring heavy-tail distribution from finite sample of histogram data

I have some data in the form of bins and counts. Here is one complete non-truncated example: ...
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457 views

High Positive Kurtosis

I'm looking at the distribution of income data examining the differences between two different surveys. I've computed medians, means std etc. Two other measures I've used are Kurtosis and Skewness. ...
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Sample Skewness and Sample Kurtosis of an exponential distribution?

Is there a closed-form expression for the distribution of the Sample Skewness and the distribution of the Sample Kurtosis of data sampled from an exponential distribution?
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Kurtosis and Skewness of Binomial Distribution

Let $X \thicksim B(n,p)$ then I would like to evaluate kurtosis and skewness of X. First I want to use the fact that kurtosis $k_3(\dfrac{X-\mu}{ \sigma})=\dfrac{k_3(X)}{\sigma^3}$ and skewness ...
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Besides skewness and kurtosis, how else can I investigate changes on a distribution?

I want to look for changes on the distribution of the laying date of a bird (i.e. if the phenology or nesting synchrony has changed). Are the coefficient of variation, skewness, kurtosis the only way ...
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Difference between long tail and short tail distribution?

I want to understand the difference between these distribution types. What is the difference between a long and short-tailed distribution?
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How to draw a sample from Johnson's distribution with given skewness and kurtosis?

I came across Johnson's system of distributions. Here, I found the following figure: The author says: There is a unique Johnson distribution corresponding to each feasible combination of $\beta_1$...
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Mardia Skewness and Kurtosis for Multivariate Normal

I have written a Matlab function to calculate Mardia's Skewness and Kurtosis. (S is the Covariance Matrix and X_bar is the mean vector.) $$b_{1,p}=\frac{1}{n^{2}}\sum_{i,j=1}^{n}[(X_{i}-\bar{X})'S^{-...
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How do I compare the skewness and kurtosis of different histograms?

I have generated histograms from each of the succeeding years. I thought of plotting the skewness and kurtosis of each to compare them. I am not sure if a qualitative description suffices to show ...
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Are Skewness and Kurtosis Sufficient Statistics?

I would like to prove that Skewness and Kurtosis are sufficient statistics for gaussian distribution. Later on I will try to prove on loglogistic distribution. Do you have any idea how to do that?
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Checking normality when there is no independence

There is a realization $(\xi_1(\omega), \xi_2(\omega), \ldots \xi_n(\omega))$ of a random vector $$ \boldsymbol{\xi}=(\xi_1, \xi_2, \ldots, \xi_n). $$ I'd like to check the following: is it true ...