Questions tagged [skew-normal]

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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Skew t student function for multivariate variables

I just learned about Skew t student function. I would like to understand one point. From the definition of this function, I see that for multivariate data, say 6 variables, the degree of freedom and ...
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2answers
60 views

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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11answers
5k views

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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53 views

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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1answer
71 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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0answers
33 views

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
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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1answer
666 views

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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3answers
2k views

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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0answers
108 views

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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1answer
109 views

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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2answers
1k views

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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0answers
100 views

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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1answer
212 views

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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2answers
829 views

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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1answer
172 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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1answer
122 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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1answer
330 views

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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1answer
56 views

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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1answer
140 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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1answer
258 views

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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1answer
148 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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0answers
1k views

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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1answer
671 views

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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2answers
3k views

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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0answers
810 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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2answers
124 views

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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1answer
654 views

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 ...
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1answer
712 views

Getting expected value from Standard Deviation and Skew?

If I have: - Standard deviation - Skew What additional information can I calculate ? Could I calculate Expected Value?
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1answer
995 views

Finding a “skew normal distribution” for given data

I am given a set of $n$ pairs $(x_i, y_i)$, where the $x$-coordinates can be interpreted as the measured values of a random variable $X$ and the $y$-coordinates can be interpreted as some "scaled" ...
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1answer
936 views

Skewness - why is this distribution right skewed?

If I interpret the accepted answer here correctly, I would say that the distribution below is right skewed (because of the points above the straight line on the far right). I don't really understand ...
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1answer
580 views

Method of moments for skew-t distribution

I'm trying to work out how to apply the method of moments to estimate the parameters of the skew-t distribution. From slide 12 of the following presentation: http://www.eief.it/files/2008/11/monti-8-...
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Skewed normal distribution where y goes to 0 for fixed values of x (0 and 1 here)

I am trying to generate simulated data for gases. For any gas I want both the highest and lowest input values to produce the outcome 0 (or very near 0). And I want the 'peak input fraction' to produce ...
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1answer
150 views

Are these models nested?

Are a standard Gaussian and a skew Gaussian nested? I'd say yes, because when we set the skewness parameter $\alpha=0$ in the skew normal we get the standard Gaussian. Also, are the normal/skew ...
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1answer
1k views

Moment-generating function or characteristic function of univariate skew-t distribution

Is there a moment-generating function or a characteristic function for a univariate skew-t distribution $y\sim ST\left(\xi,\omega^2,\alpha,\nu\right)$ as defined by Azzalini?
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1answer
280 views

Inconsistency between sample median and theoretical median for skewed normal using rsnorm in fGarch

I am using the rsnorm function within the R fGarch package to generate random samples from a skewed normal distribution. However,...
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0answers
207 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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1answer
438 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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1answer
4k views

Parameter estimates for skew normal distribution

What are the formulaic parameter estimates for the skew-normal? If you can, the derivation via MLE or Mom would be great too. Thanks Edit. I have a set of data for which I can tell visually by plots ...
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1answer
249 views

Is the skew normal distribution log-concave?

Is the skew normal distribution log-concave?
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5answers
6k views

Can I hypothesis test for skew normal data?

I have a collection of data, which I originally thought was normally distributed. Then I actually looked at it, and realised it wasn't, mostly because the data is skewed, and I also did a shapiro-...