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

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Fitting an asymmetric Gaussian

I've got some spectral data that I'm processing, but there is a clear skew in the data. What I need is to quantify how asymmetric the data is, and to plot a skewed Gaussian in order to obtain the ...
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Error bars on graph, skewed data, negative standard deviation

I have only had basic stats. I conducted some research where I have four different treatments and results for the data range from 0-6. I don't need any elaborate stats test, I just want to know how I ...
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150 views

Comparing and visualising highly skewed distributions

The data I'm working with are highly skewed, with the vast majority of data concentrated at 0. It seems really hard to highlight the differences between these kind of distributions: ...
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33 views

a perfect or symmetric bimodal distribution

I would like to know how I can measure the degree of symmetry of a bimodal distribution. Is there any a criterion like for example skewness in the case of unimodal distributions?
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Skewed response variable LM [duplicate]

I have a positive asymmetric response variable in a regression model. One of the assumptions about linear model is that the stochastic component of the model is normally distributed. If I have a ...
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29 views

Why is kurtosis of a normal distribution = 3 and skewness = 0, Mathematically

Now I understand that kurtosis = 4th moment / Std ^4 ... where the 4th moment = 3*std^4. so eventually k = 3. But for the report I am working on, my prof needs me to prove it using guassian PDF. can ...
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Measurement that the model is good enough for prediction

I hope can help me with this general question, First of all my dependent variable in the number of patents per year per firm (its a case study about 3 large pharmaceuticals). So after consulting in ...
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59 views

Fit very Skewed Data with Large Amount of Zeros in GLM in R

Problem I was hoping someone could help me fit an unusual data set which includes a large amount of 0's in my dependent variable in R. Model My goal is to find which variables (tyre brand ...
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96 views

how to determine skewness from histogram with outliers?

I have the following histogram created in Minitab. I am wondering whether this histogram is actually positively skewed, negatively skewed, or symmetric. By observing the graph itself, it seems that ...
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imbalance in sample size at multilevel longitudinal data

I have longitudinal data (BMI level) measured at 3 time points and subjects are students nested to schools. The sample size in school level differs considerably (n=85 % in school 1, n=10 % in school ...
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62 views

Incorrect Kurtosis, Skewness and coefficient Bimodality values?

This is my first post in CrossValidated and hope you can solve my problem. I've tried to calculate the bimodality coefficient (b) of two frequency distributions by using this formula: where g is de ...
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43 views

Disproportioned contingency table

I have a database of clients, some of which have gotten a special pill - and the rest have not gotten the special pill. Afterwards I measure if the clients starts exercising. My contingency table ...
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Transformations for a [0,1] covariate in polynomial regression

I have a polynomial regression in the form of $y = a + b_1x_1 + b_2x_1^2 + b_3x_2 + ...$ I am interested in the interpretation of the regression coefficients, specifically if the relationship of $y$ ...
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39 views

Transforming Negatively Skewed Independent Groups

I have two independent groups, (roughly 30 in each) – and their performance on 3 different tasks, there are 10 scores in total for each group. The majority of them are negatively skewed so I know I ...
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68 views

Whitening transformation for skewness?

Let $X$ be an $(m,n)$-matrix interpreted as a two dimensional array with each column representing $m$ samples from a random variable, with known covariance matrx $M$ and mean equal to $0$, it is ...
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38 views

Regression with negative skewed data [duplicate]

Sorry I was told that my question previously didn't contain enough detail so I'm trying to reword. I have a large dataset (circa 700 obs) consisting of a continuous response variable and a series of ...
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48 views

How to calculate skewness and kurtosis in parallel?

I wanted to know is there any way to calculate skewness and kurtosis of a set as a combination of skewness and kurtosis of its subsets ? So, For example if my data is, ...
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47 views

Transform sample to achieve target mean, skewness, etc

I have a sample of data with N values from which I calculate basic moments such as mean, standard deviation and skewness. I will then change these moments to different values according to my own ...
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27 views

Meta-analysis of skewed data with low event rate (single-arm studies)

I am trying to pool the data from several single-arm studies regarding the re-infection rate of a certain disease using STATA. From each study, I have obtained the no. of re-infections, and the ...
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30 views

Forecasting Skew & Kurtosis

I have seen several models for estimating the expected value and variance of a distribution. I am curious, to learn if anyone has looked at models that extend beyond these first two moments ...
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59 views

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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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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58 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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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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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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304 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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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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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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118 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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3answers
482 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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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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448 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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307 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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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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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 ...
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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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284 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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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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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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139 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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70 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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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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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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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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235 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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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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70 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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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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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 ...