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 ...
- 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
$$
\operatorname{Var}(X+Y) = \operatorname{Var}(X) + \operatorname{Var}(Y) + 2 ...
Tim♦
- 113k
2
votes
Accepted
Variance of OLS estimator with binary treatment
In the case of simple linear regression
$$\underbrace{\begin{bmatrix}
y_1 \\
y_2 \\
\vdots\\
y_n
\end{bmatrix}}_{Y} = \underbrace{\begin{bmatrix}
1 & x_1 \\
1 & x_2 \\...
- 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 ...
- 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
$$2\vert\text{Cov}(X,Y)\vert\le\text{Var}(X)+\text{Var}(Y)$$
...
- 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 ...
Tim♦
- 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).
$$Y \sim Poisson(\lambda)$$
$$...
- 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 ...
- 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 &...
- 51
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