All Questions
14
questions
1
vote
1
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44
views
Can we find a variance formula in terms of the log of the density? ($f(t) = e^{u(t)}$, need variance in terms of $u$)
Given a density $f(t)$, say over $t\in \mathbb{R}^n$ absolutely continuous with Lebesgue measure. Write $u(t) = \log(f(t))$ taking values in $[-\infty, \infty)$ so $f = \exp(u)$.
Can we find a general ...
- 483
1
vote
1
answer
424
views
Estimating the log-space sigma (std) parameter of a lognormal distribution from its regular-space mean and variance
validaters,
I've spent a lot of time on this issue and I can't figure it out yet.
So, a lognormal distribution is being defined as follow: X=e^(μ + σ Z), where Z is ...
0
votes
1
answer
725
views
Get Standard Deviation and Variance of log 10 data in Excel
In Excel, my data is between 0.000001 and 0.005 and treated as "logarithmic" so I transformed by log 10 (log10(x)) which are all negative.
The Excel Var.P() and Stdev.p() functions can only ...
1
vote
0
answers
21
views
Random variable with finite logarithmic first moment, infinite logarithmic variance [duplicate]
Could you provide an example of a random variable $X$ such that $|\mathbb{E}(\ln(X))|<\infty$ but $\text{Var}(\ln(X))=\infty$, if such a random variable exists at all?
Related: "Random ...
- 68.6k
2
votes
2
answers
3k
views
Getting the variance of $X$ from $Var(\ln(X))$
I've a multiplicative model for which $Y = X*Z$, for which $Y$ and $Z$ is known. I want this model to be additive (therefore using logarithms) to figure out the variance of $X$. I have $$ln(Y) = ln(X) ...
- 23
0
votes
1
answer
392
views
Fitting a logarithmic trendline on already logged values
This is the situation. I am running trials with a population simulator, which produces various outputs (y), with the variance of these outputs being dependent on the number of clones (x) (recursions) ...
- 3
0
votes
1
answer
327
views
Odds ratio, Meta-analysis
I have the following for the data for the meta-analysis:
OR , standard errors, logged OR , variance of logged OR
I have generated a forest plots first using "OR" with "variance of logged OR" using ...
- 31
0
votes
1
answer
161
views
Quantifying and communicating a variables contribution to the variation in another, where the sum or product of the variables is known exactly [closed]
Two vectors, $a$ and $b$ either sum or multiply to exactly equal $c$. How can I quantify and communicate the contribution of variance in $a$ or $b$ to the the variance in $c$? $a$ and $b$ could either ...
- 143
11
votes
2
answers
4k
views
Why does log-transformation of the RNA-seq data reduce the amount of explained variance in PCA?
I am running a PCA on a dataset with 2k rows and 36k columns. I noticed that when I log-transform the data I need to ask for more principal components during PCA to achieve the same amount of ...
- 1,247
3
votes
0
answers
574
views
Expectation of the log of a ratio of two lognormal random variables with additive constants
I have two independent lognormal random variables $X$ and $Y$ with known means and variances. I would like to know the expected value and the variance of $\ln\big((X+1)/(Y+1)\big)$. If there is no ...
- 41
3
votes
1
answer
354
views
Formula for the covariance of logs in exponential families
I could not understand and don't see how the author derived equation (16). The Covariance is with respect to a pdf $\mu_k$ for the random vector $u$. The variable $\xi$ is a ratio of two densities and ...
- 294
2
votes
2
answers
620
views
How can I calculate variance of a very large random variable?
I'm implementing an algorithm which recieves as input samples from a random variable with an unknown distribution.
The random variable is extremely large so my input is logarithmic, and still large (...
- 131
3
votes
2
answers
2k
views
Maximum Likelihood estimator of population variance and its derivation process
I have 2 questions about maximum likelihood and using it to calculate variance:
Question #1:
The question is about finding the derivative of the score function with respect to the parameter $ \sigma^...
- 419
4
votes
0
answers
130
views
Avoiding large variances when taking the logs of small values
I have two random variables $(X$ and $Y)$ that are always positive. The assumption I'm making is that their logs follow normal distributions (i.e., $N(\overline{\log(X)},s^2_{\log(X)})$ and $N(\...
- 463