Linked Questions

5
votes
2answers
3k views

Distribution of function of variable having a Gaussian distribution

If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute the distribution of $f(X)$ i.e. the resulting Gaussian distribution from this? ...
6
votes
2answers
1k views

Data transformation using copulas

I've heard about the use of copulas to transform data. For instance, supposedly it's applied to data that is non-normal to make it look more normal. However, I don't quite understand how this is done. ...
3
votes
1answer
2k views

Sum of Gaussian is Gaussian?

As a newbie in probability, I am recently cleaning my understandings about Gaussian distribution. I know that If $X$ and $Y$ are jointly Gaussian, then $aX+bY$ ($a$ and $b$ are both constant) is ...
1
vote
2answers
2k views

Python: Gaussian Copula or inverse of cdf

Let's say I have a column x with uniform distributed values. To these values, I applied a cdf-function. Now I want to calculate the Gaussian Copula, but I can't find the function in python. I read ...
3
votes
1answer
1k views

Does uncorrelation imply independence for marginally Gaussian random variables?

Let $X_1, \ldots, X_n$ be marginally Gaussian distributed random variables that are uncorrelated. Does it imply that they are independent?
0
votes
1answer
633 views

How to transform an arcsine distribution to a normal distribution?

I have a distribution that looks like this: U In other words small and big values are more frequent than middle values. A better graphical example of the distribution is this: Here So I have a ...
1
vote
1answer
539 views

How to change exponential distribution into Normal distribution? [closed]

We have random data, which is exponentially distributed. Data = exp($\lambda$), where $\lambda$ = 0.5. If it is possible to change exponential distribution into the normal distribution. Then what ...
1
vote
1answer
232 views

Is it possible for $X$ and $Y$ to be marginally normally distributed and have $ E[Y|X] $ be a nonlinear function of $X$? [duplicate]

Is this at all possible? What is the intuition for this?
1
vote
2answers
106 views

Distribution for an operation of variables with identical distributions

I have this doubt: Consider $X$~$N(\mu_X,\sigma^2)$, $Y$~$N(\mu_Y,\sigma^2)$ and $Z=X-Y$ I know that $E(Z)=E(X)-E(Y)=\mu_X-\mu_Y$ because the expected value is a linear operator. And I know that $...
5
votes
0answers
49 views

An example of a bivariate distribution with normal marginals and a nonlinear conditional mean curve? [duplicate]

That is, an example of a bivariate distribution with normal marginals for which a linear regression is inappropriate. Does an asymmetric copula always produce this?