All Questions
365 questions
1
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1
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86
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Kurtosis of the Rice distribution
The Rice distribution $X$ (over $\mathbb{R}$) is the magnitude of $\vec{X}$, where $\vec X$ is a shifted 2D normal distribution $\vec{N}$ (over $\mathbb{R}^2$).
Say the 2D normal distribution has ...
- 31
0
votes
0
answers
36
views
On the finiteness of moments of a distribution
Consider a continuous random variable $X\equiv\log(Y)$. Assume that
$$
E(\exp(\alpha X))< \infty \quad \text{ for some $\alpha>0$}
$$
I would like to understand what does this assumption imply ...
- 935
0
votes
0
answers
23
views
How to deal with high kurtosis in VAR model
I'm trying to do a VAR model on Stata to find the effect of some variables (Exchange rate, volatility, trade openess, GDP and school enrollment rate) on inflow FDI. While most of them are not ...
0
votes
0
answers
70
views
Isn't kurtosis poorly defined if it doesn't take into account skewness?
Apologies in advance, I am not a statistician so this question may be naive. The way I understand things is as follows:
The mean is the first raw moment.
Variance is the second central moment, i.e. ...
- 190
0
votes
0
answers
36
views
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-...
8
votes
4
answers
518
views
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 ...
- 435
1
vote
1
answer
52
views
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 ...
2
votes
1
answer
62
views
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 ...
- 141
0
votes
0
answers
23
views
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 ...
- 633
0
votes
0
answers
38
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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{\...
1
vote
0
answers
39
views
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 ...
- 3,247
8
votes
5
answers
2k
views
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 $M^k(0)=\mathbb{E}(X^k)$ ...
- 83
6
votes
2
answers
704
views
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'...
- 63
3
votes
0
answers
61
views
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 ...
- 330
2
votes
0
answers
143
views
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, $\bar{X}$ ...
- 435
3
votes
0
answers
126
views
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 ...
- 435
0
votes
1
answer
435
views
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 ...
- 1
1
vote
1
answer
77
views
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....
- 217
1
vote
0
answers
30
views
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 ...
- 11
0
votes
0
answers
104
views
Timeseries Anomaly Detection using Rolling Kurtosis?
I'm working on anomaly detection for multiple streaming time series datasets. Due to the vast number of datasets, I'm seeking a scalable, generalized method without resorting to adaptive thresholds ...
- 235
0
votes
0
answers
60
views
GAM: mgcv model with kurtosis: Does this need to be solved and how?
I am trying to model CO2 fluxes (fco2) using a number of environmental parameters using a GAM in mgcv. Specifically, I have leaf temperature (tl), vapour pressure deficit (vpd), and transpiration (tr)....
- 33
0
votes
1
answer
150
views
What does it mean when dots on a residual vs fitted graph are clumped like a shotgun result? How do I fix it if it needs to be fixed?
Here's the code for these graphs
...
- 1
1
vote
0
answers
51
views
Non-negative fat-tailed "almost stable" family of distribution with finite mean?
I am looking for a finite-dimensional family of distributions $F_X(x)$ with all the following properties:
Supported on $[0, +\infty)$,
Fat tailed, i.e. $(1-F_X(x)) \sim x^{-\alpha}$ for $x\to +\infty$...
- 237
3
votes
1
answer
78
views
Calculating Kurtosis for Groups Containing Fewer Than 4 Observations
Based on some preliminary exploration, here are some interesting observations about kurtosis for when you're calculating kurtosis for groups that have fewer than 4 observations. First, here's the ...
- 297
0
votes
1
answer
23
views
Can I do skewness on multiple standard deviation?
I have a 1000 sample of an electrical test at each 4 different time, so I do simple descriptive statistic to obtain standard deviation at each 4 different time. Can I then use skewness on standard ...
0
votes
0
answers
61
views
Meaning of Skewness and Kurtosis values of Residual Errors in Time Series Forecasting Problem using LSTM
I have developed different kinds of RNNs (such as LSTM,GRU etc.)to predict future values of thermocouple measurements. The residual errors look like they do not follow normal distribution, so I wanted ...
- 1
0
votes
0
answers
702
views
Cut off value of +/- 1.5 for Skewness and Kurtosis (Tabachnick & Fidell)
I've read multiple posts/papers citing Tabachnick and Fidell's cut off of +/- 1.5 as the acceptable range for skewness and kurtosis to determine normality; however, I cannot find it in their book. Can ...
- 19
1
vote
0
answers
43
views
Inaccuracies due to initial values in GARCH(1, 1) simulation
I'm experimenting with non-normal innovations standard GARCH(1, 1) model
$$\epsilon_t = \sqrt h_t z_t$$
$$h_t = \omega + \alpha \epsilon_{t-1} + \beta h_{t-1}$$
Where $E[z_t] = 0$, $E[z_t^2] = 1$, but ...
- 11
1
vote
0
answers
78
views
Does Bayesian modeling result in fat-tail distributions?
Let's say we have an univariate dataset x that follow a gaussian with parameters (m, s).
Under a frequentist methodology, m and s are estimated using MLE and x is modeled as N(m_hat, s_hat).
Using the ...
- 1,046
1
vote
0
answers
39
views
Power analysis to detect non-zero skew/kurtosis
Tests exist to determine whether a distribution is normal. For example the Shapiro-Wilk’s method. I'm wondering how to determine whether I'm powered to detect that my distribution is non-normal (e.g., ...
- 1,944
1
vote
0
answers
33
views
A question about the variance of sample variance? [duplicate]
if I have negative kurtosis in my distribution (meaning negative exceeded kurtosis) - which indicates that the tails are lighter than normal distribution tails.
Does it also mean that I have more ...
- 45
1
vote
0
answers
53
views
Is there a relationship between the alpha of fat tails and kurtosis
From Wikipedia I have the compliment of the CDF parameterized for fat-tails distributions.
$$
\Pr[X>x] \sim x^{- \alpha}\text{ as }x \to \infty,\qquad \alpha > 0.\
$$
In forecasting literature a ...
- 2,051
1
vote
0
answers
26
views
Transform a sample to have target values for the first 3 moments (Equating moments)
I want to transform the first three moments of a sample X of size N to get a new sample Y with moments ($\mu_Y, \sigma_Y, \nu_Y$). The first two moments can be mapped to the target values using the ...
- 11
1
vote
0
answers
34
views
Can we improve variance estimate by using sample kurtosis?
The sample variance is the minimum variance unbiased estimator and its variance is related to kurtosis
$$\operatorname{Var}(S^2) = \frac1n\left(\mu_4 -\frac{n-3}{n-1}\sigma^4\right)$$
Is there some ...
- 811
2
votes
2
answers
230
views
Is my data fat tailed in terms of alpha
From Wikipedia I have the compliment of the CDF parameterized for fat-tails distributions.
$$
\Pr[X>x] \sim x^{- \alpha}\text{ as }x \to \infty,\qquad \alpha > 0.\,
$$
Here $\alpha$ is the ...
- 2,051
0
votes
0
answers
68
views
Rejection Sampling Kurtosis and Number of Iterations
I tried to implement a rejection sampling method in python based on something explained during class. The target distribution is the normal distribution and the proposal is the exponential ...
- 1
1
vote
0
answers
114
views
Normality tests for latent variable in probit regression
I am performing a probit regression where the latent variable y* is conceptually important. I already have the model defined with regressors: categorical variables, quadratic terms, continuous ...
- 11
1
vote
0
answers
48
views
Kurtosis is greater or equal to square of skewness plus one [duplicate]
Given is a random variable $X$ with finite fourth moment. Let $\gamma_3$ and $\gamma_4$ denote its skewness and kurtosis respectively.
I want to prove that $$\gamma_4\geq 1+ \gamma_3^2$$
I have seen a ...
- 111
-1
votes
1
answer
1k
views
How to deal with high skewness and kurtosis
I have two dependent variables (soccer dataset) that I'm interested in. They have the following skewness and kurtosis:
Variable A: % of minutes played --> Skewness: 0.145 | Kurtosis: -1.03
...
- 63
1
vote
0
answers
307
views
How can I standardize a sample to fixed skewness and kurtosis? [closed]
Standardizing a sample of a random variable to mean 0 and standard deviation 1 are common practice. However, I would like to also standardize its skewness to 0 and its kurtosis to 3, but preserve ...
- 990
0
votes
0
answers
81
views
Does skewness multiplied by kurtosis have some intuitive meaning?
I understand the individual measures of skewness (how asymmetric a distribution is) and kurtosis (how "large" the tails are in a distribution). For this specific case, I am referring to ...
- 1,334
0
votes
0
answers
62
views
Transformation of discrete data to reduce Skew
In a dataset I have running through on kaggle's tabular playground, some of the measurement columns that are missing values follow a gaussian distribution.
I want to fix these missing values by ...
2
votes
0
answers
175
views
Probability distribution with independent expectation, variance, skewness and kurtosis
There are 4 measures for the characterization of the shape of a probability distribution: expectation (1st order raw moment), variance (2nd order central moment), skewness (expression in 3rd and 2nd ...
- 23
4
votes
0
answers
563
views
Are Poisson distributions with low mean heavy-tailed?
It is very apparent to me how using the normal distribution to estimate the probability of large, Poisson-distributed events may lead to significant underestimates of the probability of these events, ...
- 91
0
votes
1
answer
208
views
F-test and violated assumptions
I am researching the effect of parameters on energy consumption. To determine the effect of parameters, I want to use the R Studio's F-test. In this way I want to investigate if the model with the ...
- 11
0
votes
0
answers
253
views
Standard deviation and long-tail data
Sorry, I don't know the math words.
I have a data set that looks like the following. I am counting things, and the graph shows how many of each thing there is. for example, I have a LOT of thing #0, ...
- 103
0
votes
2
answers
91
views
Is there a way to define significance to say something has "fatter" tails?
I have two distributions of data. The means are about the same, but one data set has longer, fatter tails. Is there a way I can say one distribution has significantly "fatter" or "...
- 133
2
votes
2
answers
164
views
Best way to find confidence interval for a mean of a symmetric leptokurtic distribution?
I have a very symmetric distribution with kurtosis of 10 and sample size of more than 100.
Here is the Histogram https://ibb.co/ws7vBjd
This histogram was obtained by asking participants in the ...
- 23
4
votes
0
answers
159
views
Are there distributions for skewness and kurtosis? Similarly to mean (normal) and variance (chi-squared)
My question is really straightforward.
The distribution of the sample means approaches a normal distribution (CLT).
The distribution of the sample variance approaches a chi-square distribution (...
- 51
0
votes
0
answers
38
views
Which method is best?
I have an independent variable which is BMI and catagorized into
1- under weight
2- normal weight
3- over weight
4- obese
Sample size is 100
The dependent variable for group 1,2 and 3 is not normally ...
- 57