9 votes
Accepted

Intuition for why mean of lognormal distribution depends on variance of normally distributed rv

The intuition for this result comes from the fact that the exponential function is a strictly convex function. When you then impose a convex transformation on the random variable $X$, the positive ...
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  • 94.2k
2 votes

Variance of the sum of multiple random number generators

Your $n$ random number generators are like $n$ random variables. The variance of a sum of random variables $X$ and $Y$ is $$ \operatorname{Var}(X+Y) = \operatorname{Var}(X) + \operatorname{Var}(Y) + 2 ...
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  • 113k
2 votes
Accepted

Variance of OLS estimator with binary treatment

In the case of simple linear regression $$\underbrace{\begin{bmatrix} y_1 \\ y_2 \\ \vdots\\ y_n \end{bmatrix}}_{Y} = \underbrace{\begin{bmatrix} 1 & x_1 \\ 1 & x_2 \\...
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  • 637
2 votes

Variance of $\hat{\beta}$ in Ridge Regression

This question seeks information that is similar to an answer in another question here, though it is not a duplicate of that other question. Most of the present answer is adapted from the answer to ...
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  • 94.2k
2 votes
Accepted

Relationship between $Var(X)$, $Var(Y)$ and $Cov(X,Y)$ for random variables with zero mean

When $\mathbb E[X]=\mathbb E[Y]=0$, $$\text{Var}(X)=\mathbb E[X^2]\quad\text{Var}(Y)=\mathbb E[Y^2]\quad\text{Cov}(X,Y)=\mathbb E[XY]$$ and $$2\vert\text{Cov}(X,Y)\vert\le\text{Var}(X)+\text{Var}(Y)$$ ...
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  • 91.7k
1 vote

Is "Information" somehow Related to "Variance"?

Why is the "most informativeness property" useful when selecting probability distributions? It isn't. It relates to the principle of maximum entropy, that ... is based on the premise that ...
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  • 113k
1 vote

Are there possibilities to determine 95% confidence interval for right skewed data?

Usually integer data, like days, is modeled using a Poisson (or Negative Binomial) regression model, both instances of what is called a generalized linear model (GLM). $$Y \sim Poisson(\lambda)$$ $$...
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  • 51
1 vote
Accepted

Variance functions for Poisson, negative binomial

Is it possible to calculate the [coefficient] standard errors from the R output? It depends on what you mean by "the R output." It's not conceptually different for generalized linear models ...
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  • 61.8k
1 vote

Variance explained - equivalent statistics for categorical data?

Based on Dave's and Vasilis' response (I'm sorry Ben my non-statistical brain could not quite absorb your answer - which is on me) I wrote and roughly validated a python function to produce a grid of &...
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