Questions tagged [skew-normal-distribution]

A family of probability distributions that includes the normal distribution as a special case, but which generalise it by allowing the distribution to be skewed.

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Have I calculated the normal distribution standard deviation equivalent correctly from this the skew normal variance?

Purpose of this work: I have two datasets. I am trying to match one person from dataset A to one person from dataset B, for every person in dataset A. These are being matched on the age difference ...
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What test is appropriate for normality?

I would like to check the normality of nearly 400 individuals. I tried many test like Shapiro test, etc...but, not much expected results. So, Could you please tell me what is the appropriate test for ...
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Is skewness visible in the cumulative distribution function (cdf)?

The following two figures are the pdf's of four parametric distributions and their corresponding cdf's. The most left-ward blue line is clearly not skewed, while the most right-ward orange line is ...
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Central Limit Theorem and Skewed Distribution

I'm looking for a simple answer to this question relating the central limit theorem and Gaussian and skewed distributions, if one exists. I used the binomial function to generate calculations of the ...
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unable to remove skewness from my data

I am trying to remove skewness from my data, since my linear model requires it. e.g. all the columns in my data look like this after plotting a kde: my data contains, 0s, posituve and negative values....
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what skewness measure should i use to asses my data?

I am trying to assess the skewness of my data, basically i want to see which columns have high skewness and then try and transform the data to be normally distributed. I am doing this since i think it ...
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How to define a skewed distribution using mode and two inflection points? [duplicate]

I want to define a skewed distribution function and plot it in python using the mode and inflection points parameter values instead of using the mean and standard deviation. For example, I have ...
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Why does deviation from uniform distribution suggest skewed-t model may not provide adequate fits for copula model

I read a book titled "Statistics and Data Analysis for Financial Engineering with R examples". At page 203, I read the following paragraph. "Figure 8....
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How to improve upon my composite index from right skewed data in R

Do you have any advice for creating an index from right skewed-data with several extreme outliers in R. I am new to creating indexes for analysis and could use some advice on how to do it in R. So ...
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Multivariate Skewed Normal fit Maximum product of Spacing

I am trying to fit a Multivariate Skewed Normal in R given the parametrization in the sn package. Here a piece the piece of code I'm using: I first define two functions I'm gonna use: ...
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Generating random values from multivariate Skew Normal distribution (fixing slant parameter)

I'm struggling on how can I generate values from multivariate Skew Normal distribution in R, fixing the location and scale parameter and the slant parameter for the ...
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Dealing with non positive definite matrix covariance (possible numeric issue)

I'm generating random number of a multivariate skew normal distribution. Here is my code: ...
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Finding parameters of a skew normal distribution knowing only the first and last deciles and a mean

I only know Q(0.1;…), Q(0.9;…) and the mean value, so I would like to know if there’s a way to find the parameters of skew normal distribution that fit to my data. For example, Q(0.1;…)=6670, Q(0.9;…)=...
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What distribution has exactly three parameters for mean, variance, and skewness?

Common distributions usually fix their skewness. Beta distribution has two parameters to determine all of the mean, variance, and skewness. Student-T's skewness can change by some definitions but it ...
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how to adjust a skewed distribution to normal?

The Totalpoints variable of the Decathlon dataset in R is a skewed distribution. How can I adjust it to normal? ...
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Generate random values to mimic skewness

I have a actual set of data where the variables are heavily skewed, both positively and negatively. I need to generate random sample data for the values going forward. The data needs to be similarly ...
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Generating skew-normal distribution in Matlab

My apologies if this is a trivial question, but I am having trouble with this for a while now. I need to use a skew-normal distribution in research in MATLAB and the only way I found after googling ...
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How to fit a skew normal distributon to given data?

I've got some data which I want to fit it to a skew normal distribution given by $f(z)=\frac{2}{\sigma}\phi(\frac{z-\mu}{\sigma})\Phi(\lambda\frac{z-\mu}{\sigma})$ where $\phi(z)=\frac{1}{\sqrt{2\pi}...
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Parametrization of a skew-normal distribution such that negative part is constant

I was wondering, how the parameters of the skew-normal distribution (https://en.wikipedia.org/wiki/Skew_normal_distribution) would be constrained when I require that a constant part of its support is ...
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Generating random values from a multivariate skew-normal with fixed marginals

I'm generating random values from the multivariate skew-normal, and I want that the marginal distributions from this multivariate one have fixed parameters as the following: I'm generating from ...
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Density of sum of truncated normal and normal distribution

Suppose that $\varepsilon\sim N(0, \sigma_\varepsilon)$ and $\delta\sim N^+(0, \sigma_\delta)$. What is the density function for $X = \varepsilon - \delta$? This proof apparently appeared in a Query ...
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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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Sampling from skew normal copula

For a project, I wish to draw from multivariate skew normal copulas. Initially I thought my approach was correct, but now I believe it's highly unlikely that it's correct. I've read up about the ...
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Sum of squared variables equals Chi-squared implies that the variables are standard normal?

It is known that if iid $Y_1,...,Y_n \sim N(0,1)$ than $\sum_i Y_i^2 \sim \chi^2_n$. However, if we know that (independent) $Y_1,...,Y_n$ have $\sum_i Y_i^2 \sim \chi^2_n$, can we say that $Y_1,...,...
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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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Getting skew normal parameters from its moments

I have data on expenditure in dollars, and for set of countries i know average expenditure, sd, skewness. For example in country A mean=200\$, sd=100, skewness=1.5 and i want to estimate probability ...
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122 views

skew normal computation

I want to compute probabilities assuming data have log skew normal distribution (in R). As I couldn't find any package that directly computes log skew normal (as plnorm does log normal), I am ...
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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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565 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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Does 68–95–99.7 rule apply to skewed distributions as well and are they statistically correct?

I am not much familiar with statistics, but for my current simulation, I am using it to analyze my results from Monte-Carlo simulation. I understand the 68–95–99.7 rule. However, I want to confirm (...
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fitting a distribution to skewed data with negative values

I am trying to model data about altruistic behavior in a simple lab experiment. I have one value for each participant in the sample (N=479), describing how altruistic that person was. As you can see ...
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Find the error on the peak value (mode) of a skewed gaussian

I have a distribution of data that follows approximately a skewed gaussian distribution (count rate vs time). I fit the distribution with the following function in python: ...
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Logistic transform of multivariate zero-mean Gaussian

Consider a multivariate logistic-normal variable $z \sim \mathcal {LN}(\mu,{\Sigma})$, where ${\Sigma}$ is and $n$-by-$n$ positive definite matrix. I mean, for $x = (x_1,\ldots,x_n)\sim \mathcal N(\mu,...
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Sampling from Skew Normal Distribution

I want to draw samples from a skew normal distribution as part of a matlab project of mine. I already implemented the CDF and PDF of the distribution, but sampling from it still bothers me. Sadly, the ...
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Is the skew normal distribution a member of the exponential family

I'm trying to proof that the skew normal distribution ist part of the exponential family, but I cannot find a solution. So is it a member of the exponential family or are my assumptions misleading? ...
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method of moments for skew normal distribution

I have a random Variable $X$ is $ SN(\lambda)$ and is pdf is given by: $f(x)=2\phi(x)\Phi(\lambda x)$. The model of the variable X is given by:$X=\frac{1}{\sqrt{1+\lambda^2}}Z_1+\frac{\lambda}{\sqrt{...
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What's the skewed-t distribution?

I have just learned GARCH model. One condition distribution of it is "sstd". One question of my coursework is to justify if the conditional distribution is skewed. I have seen another example sheet ...
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354 views

Parametric Definition of Skewed Normal Distribution with Left and Right Percentile

Is it possible to easily build a Skewed Normal Distribution with these 3 parameters? -Mean (or median) 99.7-th Percentile for data to the left of the mean (median) 99.7-th Percentile for data to the ...
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180 views

Learn parameters for truncated Gaussian

I would like to learn the parameters for a truncated gaussian like this one. I'm using this formula for the probability density $f(x | \mu, \sigma^2) = \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) \...
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Bivariate Skewed Normal Distribution

What is the equation for a multivariate skewed normal distribution, specifically a two dimensional skewed normal distribution?
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Known univariate unimodal analytical convolution with gaussian

I have data that are distributed with an unknown distribution. The data are from one continuous variable and unimodal. The shape looks like a gaussian, but it is asymmetric and with more long tails. ...
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153 views

Show that $\log \phi(z;\lambda)$ is a concave function

Let $Z\sim SN(\lambda)$ where SN means skew-normal. Then a random variable $Z$ have density function given by $$\phi(z;\lambda)=2\phi(z)\Phi(\lambda z)\qquad -\infty<z<\infty$$ where $\...
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Show that $Y_1+Y_2$ have distribution skew-normal

Let $Y_1\sim SN(\mu_1,\sigma_1^2,\lambda)$ and $Y_2\sim N(\mu_2,\sigma_2^2)$ independents. Show that $Y_1+Y_2$ have a skew-normal distribution and find the parameters of this distribution. Since ...
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337 views

Estimate parameters for skew normal distribution

I know there is already at least one question answer with this, but I think the solution does not apply in my case. I have a population for which I know the mean, variance and skewness. I saw how to ...
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How to fit a mixed effect model to a left skewed continuous response

Does anyone have any suggestions (short of transforming my data) on how to fit a mixed effect model to a continuous response variable that is left-skewed? Other words, what probability density ...
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Finding the parameters of a skew normal distribution from quantiles

Suppose I have three quantile values of a skew normal distribution. How do I calculate the parameters of the distribution? For one simple example, suppose I know the 10%, 50%, and 90% points of the ...
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Simulating from a skew normal distribution

I am analyzing a data set in R, the histogram gives an impression of a normal distribution, but the qqplot suggests a slightly skewed normal distribution, so I want to try this out as well. I fitted ...
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982 views

Multivariate asymmetric generalized gaussian distribution

I would like to write the distribution of a multivariate asymmetric generalized gaussian distribution and plot the result with Matlab. So far I was able to write the code to create a bivariate ...
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Describing random variables: “Defined as” contrasted to “has the property of”

This was inspired by this question and the comment of user @Did to it. At first it may appear as some subtlety that would interest some educational course only. But since it relates to how we ...
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Dealing with shape parameter of standardized skew normal distribution in DCC-GARCH

Say we have a GARCH(1,1) equation such as $h_t = \omega + \alpha\varepsilon^2_{t-1} + \beta h_{t-1}$ and $\varepsilon_{t-1}$ follows a standardized skew normal distribution. Using MLE we get the ...