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Questions tagged [skewness]

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

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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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1answer
20 views

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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228 views

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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1answer
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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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1answer
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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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1answer
31 views

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 ...
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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, \...
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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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0answers
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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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1answer
66 views

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 ...
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1answer
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How do you find shape parameters of a Johnson distribution from skew and kurtosis?

I'm trying to generate random numbers from a distribution with given moments, in my field the Johnson family of distributions is typically used but I can't find anywhere how to set it's shape ...
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Modelling my own cost function for skewed distributions

A while ago I worked in a model used for fraud detection, as that involved a very asymmetric distribution, I used F1-score as my loss function. However, I cannot stop thinking about it, and I feel F1-...
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Is there any non-gaussian distribution has skewness 0 and kurtosis 3?

Is there any non-gaussian distribution has skewness $0$ and kurtosis $3$? Thanks!
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1answer
576 views

Gradient boosting regression trained on skewed data

My target feature is right-skewed. I want to apply gradient boosting regression algorithm to predict it but I'm not sure what kind of preprocessing should I apply. As gradient boosting is based on ...
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0answers
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What are some good non-negative distributions for modeling data in Bayesian inference?

I'm just currently getting into the world of Bayesian machine learning, with a lot of frequentest stats background, and I frequently find myself limited in my modeling by my lack of knowledge about ...
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High proportion of zero values and PCA

My aim is to perform PCA since I have 76 variables in my dataset. Problem is that most of my variables are highly skewed as you can see in the histogram below. These variables are proportions ...
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Zero-inflated highly skewed predictor variables

I've thoroughly searched this website and multiple others and can't seem to find an answer to my question. This is also my first post so I hope I've followed all the rules. I apologise for the length, ...
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1answer
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Density chart of S&P500

I am examining the daily log returns of the S&P500 Index and I have negative skewness and excess kurtosis. However when I chart the density plot I am seeing positive skewness - does this seem ...
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1answer
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In linear regression, data is highly skewed, transformation doesn't work..!

I have dataset with 9524 observations / 97 variables. Most of variables are numerical, and some of factor variables (Yes/no or several levels) I want to perform multiple linear regression with ...
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2answers
449 views

Application of Skewness and Kurtosis

Often in finance, stock prices are considered to follow a lognormal distribution while stock returns are considered to follow a normal distribution -prices are positive while returns can be negative(...
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1answer
82 views

Is there a skewed probability density function that models a normal distribution with two parameters, $σ_1$ and $σ_2$?

Is there a way to model data that are skew normally distributed, but for which one builds in two seperate standard deviations? The parameter $σ_1$ should specify the 15.9% to 50% interval, whereas $...
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0answers
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What is the difference between skewed logistic regression and rare event logistic regression

I was doing a traffic safety analysis. My understanding is that if I have a sample that the response distribution differs a lot. for example, I have 200 events, but only 20 of them are crashes. I ...
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1answer
60 views

Are there theoretical reasons for choosing between similar distributions?

I'm interested in estimating the distributions of a few skewed datasets, for example extreme heat, and extreme rainfall. There are many distributions that can be fit to these kinds of data, for ...
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Comparing the means of two groups when a large number of data points have the same value

I have data on the profitability of wagers made according to two different strategies. One strategy was to bet $1 on the underdogs in each of a sequence of sporting matches. They have data like this: ...
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1answer
83 views

Fitting a left-skewed curve to data [closed]

I have the following data for x and y-axis inputs. I am trying to fit a left skewed curve (i.e. long right tail) with a steep right peak to this data in R. I am not sure what curve equation to use (...
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1answer
27 views

How to draw one standard deviation range around the mean of a skewed distribution [closed]

I have a distribution of data with a positive skew, shown in the image. The standard deviation is 1.34 and the mean is 2.01. I want to illustrate on the graph the range of values that are within one ...
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1answer
160 views

Binary predictor with highly skewed distribution

I am running a linear regression model and I have a binary predictor that has a highly skewed distribution. For example, one category represents 96% of the data. In terms of frequency, the other 4% ...
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3answers
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An oddly skewed distribution of p-values

I stumbled upon an odd result which I have difficulties to explain. In the following code, $x_1$ and $x_2$ are very similar variables. Yet the distribution of p-values for the coefficient in $x_1$ is ...