Questions tagged [kurtosis]
a normalized fourth moment of a distribution or dataset, or other aspects of fat tails
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Kurtosis of b(n,p) - binomial distribution
So I have this problem that I’m trying to do.
I been at this for hours.
It’s to find the kurtosis of a binomial distribution.
So far, I have that M’’’’(0) = $n[(n-1)(n-2)(n-3)p^4 + 6(n-1)(n-2)p^3 +7(n-...
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Estimate Box-Cox Transformation Lambda Using Skewness and Kurtosis
I would be interested in a method to find an appropriate Lambda parameter for the Box-Cox transformation based on only the skewness and the kurtosis of a given sample.
I.e, if the skewness and ...
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Derivation of a dynamical Generalized Pareto distribution
I'm currently reading a paper for my master thesis on the tail index estimation for asset returns using the peak over threshold method. In this paper the authors introduce the cumulative distribution ...
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Why do the skewness and kurtosis formulae have powers of the variance in the denominator?
We calculate the variance as the centered 2nd moment $E[(X-\mu)^2]$.
So when it comes to the skewness and kurtosis, why are the 3rd and 4th moments divided by the 3rd and 4th powers of $\sigma$? Why ...
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occurence of a n-sigma event in symmetric distribution
Is it possible to approximate the frequency of occurence of a n-sigma event in a symmetrical (skew=0) unimodal distribution with mean/mode/median=0, but with fat tails, with given kurtosis =k.
I was ...
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Inequality regarding measure of skewness & kurtosis [duplicate]
The measures of skewness and kurtosis respectively are
$b_1=\frac{m_3^2}{m_2^3}$(skewness)
and
$b_2=\frac{m_4}{m_2^2}$(Kurtosis)
where $m_r$ is the central moment of $rth$ order. That is $m_r = \frac{\...
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How should I best to use reported stats on the Tippy-top?
Suppose I have a large population, in the millions, drawn from some underlying distribution, which we will take as a member of a known distributional family with unknown parameters. Assume the ...
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How can we efficiently find the fourth moment of a Poisson distribution?
Suppose we have $X\sim \textrm{Poisson}(\lambda)$ and we know that moment generating function $M(t)=\mathbb{E}(e^{tX})$. How do we use the moment generating function property $M^k(0)=\mathbb{E}(X^k)$ ...
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Finding a distribution where skewness and kurtosis do not depend on each other. Does it even make sense?
I am simulating non-normal data to investigate how this affects some diagnostical methods that assume normality. In particular I'm interested in seeing how skewness and kurtosis affects the results.
I'...
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Formal testing for differences in kurtosis between two samples when bootstrapping suggests a difference
My question is similar to Testing difference in kurtosis between two samples where a comment suggested
Unless you are looking for an enormous difference in kurtosis, it's
unlikely any physically ...
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Variance of Fourth Sample Central Moment [closed]
I am trying to derive a formula for the variance of the fourth sample central moment $m_4=\frac{1}{n}\sum_{i=1}^n (X_i-\bar{X})^4$ (where $X_i$ is the $i$th realization of a random variable, $\bar{X}$ ...
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Pooled Kurtosis Estimator Using Pooled Cumulant Estimators
I am trying to come up with a statistically sensible pooled kurtosis estimator that is based on pooled cumulant estimators.
Specifically, I have unbiased estimators of the second and fourth cumulant ...
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Can you do a log transformation for excess kurtosis, or is that mainly used for skewness?
I am planning on doing a regression analysis on STATA on the financial performance of private equity funds. On my descriptive statistics, I saw higher levels of kurtosis and skewness. I decreased ...
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Probability that a sample drawn from one distribution is lower than a sample drawn from another distribution?
Context: we don't know the exact distribution parameters, however in practice
we can obtain many samples from each distribution.
Case 1: let's say that I have a sample of size N from each distribution....
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Spliced Distributions Framework for python
There is an article Fat-Tailed Regression Modeling with Spliced
Distributions
that describes fat-tailed regression modeling by fitting the distribution consisting of N components (different ...
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