Skewness measures (or refers to) a degree of asymmetry in the distribution of a variable.

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Does skewness predicts variance?

(with apologizes to this question). Consider two distributions $G$, $F$ both uni-modal and absolutely continuous, square integrable and satisfying: $$F<_c G$$ this means that the standardized ...
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19 views

Best method of analysis for negatively skewed longitudinal environmental data?

I have a dataset composed of a dependent variable (species percent cover) and a range of abiotic variables (salinity, temperature, pH, water movement etc). It is a longitudinal study, in which species ...
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28 views

Log form of variables and descriptive measures

Because of larger values of variables, I did a log- transformation in my dataset. Now I want to give a descriptive table regarding my variables like mean, max, min, median, skewness, kurtosis. Can I ...
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142 views

Relationship between skew and kurtosis in a sample

It is well known that $\text{excess kurtosis} \geq \text{skew}^2 - 2$, at least in a population. However, what is the relationship between skew and excess kurtosis in a finite sample? Define excess ...
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82 views

Hypothesis test for correlation between Gamma random variables

I have two Gamma random variables. I need a hypothesis test to detect a possible correlation between them.
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101 views

Departure from normality assumption in ANOVA: is kurtosis or skewness more important?

Applied linear statistical models by Kutner et al. states the following concerning departures from the normality assumption of ANOVA models: Kurtosis of the error distribution (either more or less ...
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12 views

Compare convergence of optimization methods

I need to quantify how 2 optimization methods differ in convergence. When training a neural network I get the following plots, which show an error function after each gradient update. I think the ...
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61 views

What kind of a distribution is the total spend of a potential customer?

I'm trying to figure out how to analyse the data which consists of a number of visits to a website and the total amount the visitor ends up spending there. There are obviously a lot of zeros - people ...
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90 views

Bootstrap confidence intervals

I write to you for 3 questions. I want to calculate confidence intervals on different measures of association (Pearson's correlation coefficient, Cramer's V and the Eta-square). I will make the ...
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123 views

Standard deviation to describe variation in positively skewed data?

I'm wondering how useful the standard deviation is when applied to positively skewed data? The standard deviation implies that 68% of data will lie within one standard deviation of the mean, but ...
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15 views

How to measure the efficiency at finite sample of a skewness index?

Suppose I wanted to know which of the skewness indexes 2 to 7 listed here is most precise in finite samples of fixed sizes drawn from a known skewed distribution. How could I do this using ...
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205 views

Outlier Detection on skewed Distributions

Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions ...
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217 views

Are there normalized equivalents to Skewness and Kurtosis?

What would be the normalized equivalent to Skewness that would have the same unit as the data? Similarly, what would be the normalized equivalent to Kurtosis? Ideally, these functions should be linear ...
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11 views

is a network the sum of its subnetworks?

I was wondering if networks/graphs are the sum of their parts. Let's say you have a 15-node network. The spectral density of that network has X kurtosis and Y skewness. You also have a 20-node ...
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46 views

Rainfall data, skewed with zeros

I would love some insight on how to treat daily rainfall data that is highly skewed with many zeros. I would like to use the rainfall data as a regressor of a logistic outcome. I do plan on ...
2
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1answer
72 views

t test with log transformation

One of my variables to be compared in a t-test is normally distributed, while the other is non-normally distributed. What test should I use? I thought I should do a reflect log10 transformation on the ...
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1answer
114 views

How to transform continuous data with extreme bimodal distribution

Is there a way to transform a continuous predictor variable (grant) that has a bimodal distribution into a normal distribution (see density plot below)? I have tried log(x+c), z-score and inverse ...
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31 views

Existence of a specific linear combination of independent random variables (stochastic representation of the flexible skew normal)

Suppose to have two standard normal variables $X$ and $Y$. I would like to find something as $Y= aR+\sum_{i=1}^k b_kC_k$ (1) (k can be 1,2 or whatever) where $a,b_1, \dots , k$ are appropriate ...
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45 views

ANOVA comparing transformed data (with a constant) and untransformed normally distributed data

I am using an ANOVA to compare a number of outcome measures. Some of these are skewed and I've used a log10 transformation for them. As some of the values are zeros I've also added a constant of 1 in ...
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130 views

Should additional crime reports about someone change our level of doubt about an initial crime report?

Edit: Note that this question is not about multiple unreliable witnesses to the same incident, but rather multiple incidents with only one witness each. Should the accumulation of separate alleged ...
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54 views

More flexible bell shape than log normal distribution

I am looking for a very flexible bell shape function, with asymmetry on both sides of the bell, also with the possibility that the left arm of the bell had a milder slope while the right had a steep ...
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39 views

Should a BoxCox transformation to normalize the skewness of data be applied to all the predictors?

If there are few predictors that are highly skewed among a larger set of predictors in case of a linear regression problem, should a BoxCox transformation be applied to only these few predictors or ...
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52 views

Skew of p-value distribution under composite null hypotheses

On this page it says ...if HA holds, the p-values have a distribution for which values near 0 are more likely than values near 1. However the p-values may have a distribution that is not ...
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54 views

When to use skew normal regression via MCMC (mixture models)?

When do I use skew normal or skew t regression via MCMC? Do I use them when the data are heavily skewed, for example income data? Or do I fit a normal regression model first and inspect the residuals ...
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190 views

When can a continuous variable be treated as categorical?

I have a continuous variable, which can take any value between 0 and some large, though not infinite, number. Let us assume that the maximum possible value is 1000. The values are nowhere near ...
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16 views

How to approach logistic regression on skewed dataset [duplicate]

I have a dataset with about 1M negative examples and 4700 positive examples. I'm trying to create a classifier that tries to predict the % of an example being positive. Given how much the data is ...
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46 views

GEE with exchangeable working covariance vs. GLM and using Clustered Robust standard errors?

I'm analysing a dataset including 100 individuals. These 100 individuals provided self-reported depression sores on equally spaced 4 occasions (every three months). The main independent outcome is ...
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Estimating necessary sample size

I am pretty new to statistics and I'd like to get pointers on the correct way to do this. I have a dataset in which I'm interested in the 50th and 90th percentile. I'd like to take a sample of that ...
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45 views

CDFs for Right-Skewed Distributions

How does one determine the percentage of a sample less than or equal to some x value for a set of discrete data that appear to be right-skewed? For example, I have a number of data points, and if I ...
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40 views

Upper bound for asymmetry using skewness

Can the following quantity be upper bounded by the (standardized third moment) Skewness of $X$ ($\mu_3/\sigma^3$)? $$\left|\mathbb{P}(X \geq \mathbb{E}X) - \mathbb{P}(X \leq \mathbb{E}X)\right|$$ I ...
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20 views

Percentage Beyond a Given Value for Empirically Defined Distribution

It is my understanding that standard deviation does not work well as a measurement for distributions that are heavily skewed. If I have a heavily right-skewed distribution, should I simply use the ...
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107 views

Regressions with long-tail variables (GDP, etc)

It seems common to apply standard linear regression to variables with long-tail distributions, like GDP, by first taking the log. What is the justification for doing that? Is it effectively assuming a ...
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47 views

GEE model for repeated skewed outcome and group mean centered time varying covariates

I have used GEE approach (log link with gamma distribution) to explore factors that are associated with outcomes of interest. My primary outcome of interest is highly skewed costs associated with an ...
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115 views

Skewness of a random variable that have zero variance and zero third central moment

If I have a random variable $x$, and the only information I know about it are: $$ m_1=E[x]=c, \mu_2=var(x)=0, \mu_3=E[(x-m_1)^3]=0$$ Can I conclude that the function distribution is symmetric about c? ...
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387 views

Proof / derivation of skewness and kurtosis formulas

Can anyone explain to me where the formula of skewness or kurtosis comes from? (I mean its derivation.) What's the logic behind it? Who proved it?
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37 views

Is this poor transformation advice for predictive modeling?

I have gotten some advice from a PhD statistician on doing predictive modeling on large datasets (lots of variables AND lots of observations) that I should perform transformations to eliminate ...
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37 views

Non-normal data (ceiling effect) and intraclass correlation

I am wondering if there is any way of doing an intraclass correlation, two-way, mixed, with non-normal data (in this case a ceiling effect)? Alternatively, what the interpretation (if any) would be? ...
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Should I use t-test on highly skewed data ? Scientific proof, please?

I have samples from a highly skewed (looking like an exponential distribution) dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want ...
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21 views

Skewed variable - better log10 or ln? [duplicate]

I am building a logistic regression model and one of my independent variable sis heavily skewed. Is it better to use the ln or the log10? Why? And how to correct the skewness of a variable that ...
3
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1answer
62 views

Compare skewness of many distributions with few observations

I have a dataset with page view data for about 500,000 users, divided into two groups. Each user can visit up to 5 pages, each as many or as few times as they want. So for each user, I have the ...
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38 views

How to improve results when using sampling in skewed binary classification?

I am using a data set with 18 features with True/False output (Related to mobile ad targeting). True values occurs only 0.4 % of the time. So, I have used sampling to keep the ratio of True and False ...
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122 views

How to deal with a skewed class in binary classification having many features?

I am doing data analysis in the mobile ad targeting domain. I have around 18 features and for a combination of these features, the result is either True or False (1/0) depending on whether the ...
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141 views

What is the reason the $\log$ transformation is used with right-skewed distributions?

I once heard that log transformation is the most popular one for right-skewed distributions in linear regression or quantile regression I would like to know is there any reason underlying this ...
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24 views

Computing the Correlation with Skewed Repeated Measures Data

Suppose I have two variables (e.g., Blood Pressure and Cholesterol) and I want to investigate their association across time. Also suppose that each individual has been measured three times ...
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80 views

Is it possible to build a curve with a given skewness and kurtosis?

I have data in the following form: Day Kurtosis Skewness Total Inflows 163 .3 .5 435670 I'm attempting to do some modeling of an inflow ...
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88 views

Skew normal approximation of Poisson distribution

What is the skew normal approximation to Poisson($\lambda$)? Am I doing this wrong?
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64 views

selecting the bins for extremely skewed data

I have a data that exhibits nearly a power law distribution, and I want to know a good binning technique to summarize the statistics. For example consider the following data: $$ \begin{array}{rr} ...
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67 views

Match Right Skewed Distribution to Normal

I am running a simulation. One of my parameters is sampled from a normal distribution. I would like to perform a sensitivity analysis using a right skewed distribution. This is what I had hoped to ...
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Probability distribution for right skewed data

My question is very similar to this previous post. I'm searching for the right distribution family to use in a GAM. My data are disease occurrence on benthic organisms (continuous response variable) ...
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133 views

Left skewed distribution implementation generalized linear model

I am very new to modelling and I have a question. I am using a generalized linear model (glm) for my data in R. My response variable is however skewed to the left ...