# Questions tagged [kurtosis]

a normalized fourth moment of a distribution or dataset.

174 questions
1answer
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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 ...
0answers
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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 ...
1answer
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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" ...
1answer
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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 ...
1answer
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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 ...
2answers
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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?
1answer
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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 ...
4answers
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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!
1answer
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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 ...
2answers
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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(...
1answer
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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-...
3answers
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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: ...
1answer
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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) ...
0answers
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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 ...
0answers
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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 ...
0answers
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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 ...
1answer
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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 ...
0answers
52 views