# Tagged Questions

Refers to a quantity to measure how strongly peaked a distribution is.

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### Kurtosis and fat tailed distributions

We all know Leptokurtic ~ Kurtosis > 3 and Platykurtic ~ Kurtosis < 3 I am bit confused about the shape of the curve. Somewhere I had read that since the area under the curve should be 1, for ...
83 views

### Outlier detection using Medial Rule

I have a data set captured every minute. Using Tukey's test for outlier detection (i.e., if number points above Q2+2.3IQR is above 10% of total distribution) then I mark the one minute window as ...
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### How to improve location and scatter estimation conditioning on higher order statistics?

Using sample moments, how can the mean and variance estimators be improved if e.g. skewness and kurtosis are known exactly? And what about using estimates for these instead, which should imho be of no ...
340 views

### Differences in kurtosis definition and their interpretation

I have recently realised that there are differences in the kurtosis values provided by SPSS and Stata. See http://www.ats.ucla.edu/stat/mult_pkg/faq/general/kurtosis.htm My understanding is that the ...
155 views

### How can I visualise a distribution that is univariate normal but bivariate non-normal?

I used the MATLAB code written below to create the following probability density function. It creates the familiar hill-shaped distribution. I'm interested to see (whether via MATLAB code or just ...
227 views

### Transformation of leptokurtic data

I'm working on my BSc dissertation currently. One of my variables is created using the ratio of one continuous (mostly) normally distributed variable to another. The distribution of ratio is very ...
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### Simulating multiple linear regression

I would like to simulate a multiple linear regression model using R. If I have the skewness and kurtosis for the residuals, how can I do that?
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### Calculating Kurtosis with Beta distribution in R

I am working on an assignment question in R. The problem I am having is to calculate the Kurtosis using Beta distribution. So far I am able to get the kurtosis value of ...
174 views

### Kurtosis of a standardized Student's-t distribution?

I use the generalized form of the Student's-t distribution: \begin{align*} f(l|\nu ,\mu ,\beta) = \frac{\Gamma (\frac{\nu+1}{2})}{\Gamma (\frac{\nu}{2}) \sqrt{\pi \nu} \beta} ...
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### Do skewness and kurtosis uniquely determine type of distribution?

Inspired by this answer, I have following question: Is it enough to know just skewness and kurtosis in order to determine distribution that data comes from? Is there any theorem that implies this? ...
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### High kurtosis, skewness and outliers

Currently I am working on my master this which is about excess returns (Sharpe ratio) of Asian REITs. I just transformed all the data in variables which are ready to use in SPSS. In the panel data ...
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### Can an estimator of the mean of a distribution with no variance have a variance?

Suppose you have a sample from a distribution with a mean but no defined variance, like the Pareto with tail parameter between 1 and 2, or Studentâ€™s t with 2 degrees of freedom. Can an unbiased ...
140 views

### t distribution method of moments

This is a further question to my original question, where I did not get an helpful answer (at leas not helpful for me) :Methods of moments for t distribution I want to fit a t distribution to my data ...
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### How to create a random variables in a simulation using skewness and kurtosis as well as average and standard deviation input?

I am curious to learn whether there are any best practises in creating random variables for a Monte Carlo simulation using input such as skewness and kurtosis information of a particular distribution. ...
527 views

### “Peakedness” of a skewed probability density function

I would like to describe the "peakedness" and tail "heaviness" of several skewed probability density functions. The features I want to describe, would they be called "kurtosis"? I've only seen the ...
645 views

### Transformation to increase kurtosis and skewness of normal r.v

I'm working on an algorithm that relies on the fact that observations $Y$s are normally distributed, and I would like to test the robustness of the algorithm to this assumption empirically. To do ...
258 views

### High kurtosis and bad skewness

Is it necessary to have normalized data if you want to apply a dynamic correlation coeffient? should the explanatory variables in the dcc method also be normalized? My dataset has a high kurtosis and ...
83 views

### Data transformations of scales

Could really do with some help from someone with more stats expertise than I have. I have some data relating to a customer survey along a range of measures which are consolidated into a number of ...
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### Permutation test to test significance of skewness/kurtosis of two distributions?

To test the significance of the skewness difference between two distributions with $N_1$ and $N_2$ samples, would the following test work: Create a single array of all the samples from both ...
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### How do I quantify a discrepancy which only exists in a subset of data?

I was looking at two different correlations (BU-OEU and BC-OEC), and found them both to be significantly negative (see Figures 1 and 2). However, eyeballing the data for the low end of BU and BC ...
1k views

### Are data transformations on non-normal data necessary for an exploratory factor analysis when using the principal axis factoring extraction method?

I am developing a questionnaire to measure four factors which constitute spirituality, and I would like to ask the following question: Are data transformations on non-normal data necessary for an ...
150 views

### Gigantic kurtosis?

I am doing some descriptive statistics of daily returns on stock indexes. I.e. if $P_1$ and $P_2$ are the levels of the index on day 1 and day 2, respectively, then $log_e (\frac{P_2}{P_1})$ is the ...
2k views

### Kurtosis/4th central moment in terms of mean and variance

Is it possible to express the kurtosis $\kappa$, or the 4th central moment $\mu_4$, of a random variable $X$ in terms of its mean $\mu = E(X)$ and variance $\sigma^2 = Var(X)$ only, without having to ...
569 views

### How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I have already posted this question in the quant section, maybe the statistics community is more familiar with the topic: I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g.page 130 ...
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### At which extent can standardized moment be trusted in comparison to plotting data?

Motivation I am interested on using R to do data analysis on a considerable amount of data. Having to plot each time I want to observe if it fits any particular distribution by eyeball (which can be ...
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### How to assess normality in variables to determine whether to use Pearson's correlation or Spearman's r (or Kendall)?

I have one dependent variable and am trying to see if any of my 12 independent variables correlate with it, however I need to check everything for normality. I understand I need to look at skewness ...
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### Types of inverse transformations

In performing an inverse transformation to correct for skewness/kurtosis in SPSS, it asks me to choose what "type" of inverse transformation and I have no idea what the differences between these ...
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### What order preserving transformation makes data more evenly spread, decreasing the peak, and fattening the tails of the distribution?

How can I transform a variable (non linear transformation) such that its values are more evenly spread, that is reduce the peak in the middle of the histogram and move more into tails?
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### Using kurtosis to assess significance of components from independent component analysis

In PCA eigenvalues determine the order of components. In ICA I am using kurtosis to obtain the ordering. What are some accepted methods to assess the number, (given I have the order) of components ...
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### Closed form formula for distribution function including skewness and kurtosis?

Is there such a formula? Given a set of data for which the mean, variance, skewness and kurtosis is known, or can be measured, is there a single formula which can be used to calculate the probability ...
816 views

### Treatment of outliers produced by Kurtosis

I was wondering if anyone could help me with information about Kurtosis (i.e. is there any way to transform your data to reduce it?) I have a questionnaire dataset with a large number of cases and ...
1k views

### Exponential weighted moving skewness/kurtosis

There are well-known on-line formulas for computing exponentially weighted moving averages and standard deviations of a process $(x_n)_{n=0,1,2,\dots}$. For the mean, \$\mu_n = (1-\alpha) \mu_{n-1} + ...
823 views

### Is sample kurtosis hopelessly biased?

I am looking at the sample kurtosis of a fairly skewed random variable, and the results seem inconsistent. To simply illustrate the problem, I looked at the sample kurtosis of a log-normal RV. In R ...