# Questions tagged [skewness]

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

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### how to detect ouliers in skewed data(left skewed distribution) [duplicate]

I have studied a lot of ways of dealing with outliers of normal or multidimensional data. But my problem is about skewed data. How can I find outliers for data with a skewed distribution to the left?
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### Skewed outcome variable, sem model: is it a problem?

My outcome variable is really skewed, and I want to include it in a SEM model (I am using lavaan - R). It is measured with a 7-points Likert scale (agreement) and consists of 5 items. If the model ...
1answer
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### What is the type of this distribution :$f(t,\beta ,\mu , \theta )= \frac{\sqrt{\pi}}{2} e^{\theta(t-\mu)^{\beta}},\theta >0$ on unit interval?

This question is related to my question here Which is answered by Martijn Weterings showning that is closed to truncated Generalised Gaussian distribution for negative $\theta$ values , My question ...
1answer
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### How to identify if my data set is skewed or not?

I think my assumptions are a bit naive regarding this matter. I have two metrics about my data set: the number of items and the cardinality of the items. Low cardinality means a lot of repeated items ...
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### Find probability between $-\infty$ and $0$

The graph shown below is the numerically result of differences of Normal Distribution ($N(15.5 , 0.60^2))$ and Exponential Distribution $(\exp(0.5))$ (Both are independent). I am trying to find the ...
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### Pooling Skewness, Kurtosis, and/or Shapiro Wilk Values in a Multiply Imputed Database

I am currently screening a database that has undergone multiple imputation (20 iterations). Unfortunately, SPSS does not provide pooled values for the Skewness, Kurtosis, or Shapiro Wilk. I am ...
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### Skewness and kurtosis of product of random variables? Analytically please?

We have two random variables, one is normal variables and other is exponential variables (both are independent). If we multiply both one, then what would be the Skewness and kurtosis of product two ...
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### Transform right skewed distribution to normal [duplicate]

My datasets histogram is the following: It contains a lot of zeros, that is why the high bar around zero. How can I transform this to a normal distribution? My problem is that the high bar coming ...
1answer
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### What if we take the logarithm of $X$ ? How does skewness and kurtosis change?

Motivated by this question, Let $X$ be a random variable. What if we take the logarithm of $X$ ? How does skewness and kurtosis change of $X$ changes compared to $\ln{X}$ ?
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### Interpreting Shapiro-Wilk-Test, skewness and kurtosis in the light of a qqplot and histogram

Currently I'm trying to find out if my data with n=11 follows a normal distribution to decide how I process further. To find this out I use the Shapiro-Wilk-Test which gives me p < 0.05 and thus I ...
0answers
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### Small sample size with very skewed right response [duplicate]

I have a dataset of 300 observations with 7 predictor variables with 1 continuous response variable. The response is strongly skewed to the right and there are no significant correlations among any ...
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### How to Incorporate Skew Into Simulated Data?

Suppose I have a dataset $\mathbf{X}$ which is a $n \times m$ matrix of $n$ independent realizations of some $m$-dimensional random vector $\mathbf{x}$. I want to generate a new dataset $\mathbf{X}'$ ...
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### Measuring the effect of a variable across a threshold

Within my data I am trying to assess whether the response variable increases as we move across different thresholds. The difficulty is that the response variable also increases exponentially as a ...
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### Modelling births as an outcome of population diversity as opposed to population size

I wish to model and estimate the relationship between population diversity and births (or birth rates) across populations, with panel data, and I face several challenges. 1) Births, population size ...
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### Log-Normalization of skewed data before feeding to neural network models ( autoencoders)

If your input data has few columns that are extremely skewed, It is well known that one would log normalize ( take log and then normalize or standardize) the data before passing to regression ...
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### Are the skew-normal distribution and the skew-Cauchy distribution heavy-tailed?

I think the title is self-explanatory. I understand that the skewness and the tail behavior of some distribution are completely unrelated as any symmetric distribution will have a skewness of zero ...
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### Kfold validation of skewed data

I'm working on a data which is skewed,I was trying to use cross validation but since most of my data is in just 1 of 6 classes when using cross validation some folds don't contain samples from all 6 ...
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### ARL0 and ARL1 EWMA control chart for simulation skewed data in R

I encounter problems when using r programming to run my code. In my study, I use robust estimator Sn,MAD, IQR and Biweight standard deviation for skewed data. In theory my ARL0 by using robust ...
1answer
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### why my in-sample predictions have very large skew? $y$ has a very nice bell shape?

I am running a LASSO regression. What makes me feel strange is that, although $y$ has a very nice bell shape, my prediction $\hat{y}$ is highly skewed to the left, i.e., a positive skew. I had ...
2answers
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### What is a symmetric distribution symmetric about if it has zero skewness? [duplicate]

We know that a distribution with zero Skewness are symmetric. A quick Google search or looking up in textbooks says that Symmetric distributions are distributions where the left side mirrors the ...
1answer
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### Which regression model for percentage data with many zeros and ones?

I am analysing the share of a tree species at different forest locations. The data I am using is in percentage of the total species composition and I am modelling it based on the climatic probability ...
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### Fitting right skewed data using maximum likelihood models?

I have this data that predicts female for increasing number of females (x-axis). Currently, I have fit a regular quadratic function, however it does not seem to estimate it well. I want to fit a ...
1answer
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### Partial skewness (kurtosis)

On Wikipedia one can read: In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random ...
1answer
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### A good measure for skewed values

I have a table with the list of values as shown below. A Model Number is like a parent Disease. The below table can be read as Patients under Model Number 200(Stroke) are 2.456 more likely to have ...
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### Unbiased Estimator of the Error Third and Fourth Central Moment in Regression Analysis

In linear regression an unbiased estimator of the error ($\epsilon$) variance is given by: $$MS = \dfrac{1}{n-p-1}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}$$ which is the sum of squares of ...
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### Right-skewed distribution with mean equals to mode?

Is it possible to have a right-skewed distribution with mean equal to mode? If so, could you give me some example?
1answer
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### Multiple Imputation of Coarsened/Interval Data

I'd like to know how to impute non-normally distributed data from interval data, where the intervals differ across different individuals. The variable I am interested in is the number of months an ...
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### Repeated Measures 2 Way Anova with non-normal non-balanced dataset

I'm doing an experiment where I test participants of two groups (experts/non-experts) under two conditions (eyes opened/eyes closed). From these tests I got 11 variables I want to compare between ...
1answer
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### Is it possible to calculate percentiles in skewed distribution without raw data (only mean, median, SD)?

If it is of any one's interest, the data is taken from the duration of men "last in bed" as studied here. I want to calculate the percentiles (say, 95th) of a non-normal distribution without raw data....
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### Is a distribution that is normal, but highly skewed, considered Gaussian?

I have this question: What do you think the distribution of time spent per day on YouTube looks like? My answer is that it is probably normally distributed and highly left skewed. I expect there is ...
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### Why might a p-value distribution have bump in middle? (genome-wide association study)

I'm working with data from a genome-wide association study. Initially, I obtained a p-value distribution as below, with a left skew indicating that a covariate not included in the model affects the ...
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### Does a log transform always bring a distribution closer to normal?

I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons). When I plot the log of the data instead, the distribution ...
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### What are the units of a medcouple?

Let's say I have a distribution of some weights in kg. I want to estimate the skewness of this distribution using a robust statistic, the medcouple [ G. Brys; M. Hubert; A. Struyf (2004). A robust ...
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### Significance Tests - Why Would a Low Sample Size Cause Problems?

Okay, on my AP Statistics test on the chapter on significance tests, the following free response question appeared: When the manufacturing process is working properly, NeverREady batteries have ...
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### Measures of central tendency for right-skewed size distributions

Suppose we are looking at a right-skewed size distribution such as the distributions of income, casualty losses, or flood sizes, and we want to look at some alternative measures to jointly represent ...
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### EFA with heterogeneously transformed variables

Can I perform an EFA (oblique rotation) with variables that have undergone different types of transformations? Can I still interpret the factor loadings and other output coherently? For ...
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### Does statistical significance impact uplift calculation for marketing campaign

I'm trying to understand 2 things in relation to calculating uplift from a marketing email campaign: Impact of statistical significance Impact of highly skewed data on calculating uplift The ...
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### Skewness Impact on Classification

I have a dataset with 134 attributes and my goal is to build a binary classification model. While exploring the dataset, I found that there was high skewness present in the attributes. I wanted to ...
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### Central Tendency for Negatively Skewed Data

I am trying to understand how to best describe left or negatively skewed data in terms of central tendency. I have provided code below that simulates such a distribution, as well as the source code ...
1answer
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### Distribution to use in a regression with a positive skewed variable with many zeros (homicide rates)

I want to study the determinants of homicide rates. However, I see when exploring the data that my dependent variable (homicide rates) has many zeros and is positive skewed. Which distribution family /...
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### Variance of squared truncated normal

What is $$\text{var}\left[v+\frac{1}{2} X \left(\frac{v-\mu}{\sigma}\right)^2 \mid v \leq \mu \right],$$ where $v$ is normally distributed $\mathcal{N}(\mu,\sigma)$ and $X>0$?
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### Higher moments of linear regression residuals?

I previously asked this on Math StackExchange, with no success, but this post will add to that with some simulations. Background In the following linear regression with i.i.d $\epsilon_i$ \$(i = 1, \...
1answer
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### Violating the assumptions of one sample t-test and wilcoxon's sign test

As far as the background of my research is concerned, I developed a framework for sustainability management in organizations through a systematic review of literature and sustainability reports. That ...
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### Is there a probability distribution with unskewed confidence intervals for quantile estimation?

The so-called process capability index Cpk is often used to express the yield Y in a production, e.g. for a given upper specification limit x. Mathematically it is based on fitting a normal ...
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### How to compare rigth skewed data with non-parametric test?! Which test is the right one

Hi im trying to compare cells size from multiple locations. I have 5 biopsy locations from 25 individuals = 125 single tissue biopsies. The cell size is aquired using digital image processing and one ...
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### how to resolve skewness problem in regression

I'm working on a regression problem. The dependant variable is skewed and has a distribution as below I'm applying the log transformation but the resulting data is also skewed and is like below. ...
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### Can two different distributions have the same value of mean, variance, skewness, and kurtosis?

Assuming that you have two discrete population distributions. Can they have identical values of mean ,variance, skewness and kurtosis while being different in shape visually ? Do these four values ...
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### What is the relationship of skew and sample size on the sampling distribution?

I'm interested in the relationship between a distribution's skew and the sample size needed for the sampling distribution to be approximately normal. Let's assume the distribution is unimodal. In ...
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### Skewness and Kurtosis estimation methods [closed]

In finance time series literature ARCH and GARCH models are used to get an estimate of volatility. Are there similar models to estimate skewness and kurtosis?
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### Sufficient sample size for skewed populations

I have measured 50000 individuals from a certain population, and 800 (~1.6%) of them have a certain characteristic (say green eyes). I can be pretty sure that this is an effect that is present in a ...