# Tagged Questions

A lognormal distribution is the distribution of a random variable whose logarithm has a normal distribution.

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### Why is the arithmetic mean smaller than the distribution mean in a log-normal distribution?

So, I have a random process generating log-normally distributed random variables $X$. Here is the corresponding probability density function: I wanted to estimate the distribution of a few moments ...
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### Get covariance from conditional covariance for lognormal (and other) observations?

Consider lognormal random variables $X_1$ and $X_2$ with correlation coefficient $ρ$ and a partial observation sample of them of length N, the sample being partial because it only contains occurrences ...
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### log percent change of univariate data

wondering if you can help me decide on the right metric to report. I am comparing multiple treatments, the measured variable is logarithmic so I take the log of my measurements and do ANOVA on the ...
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### What are some of the more popular variable transformations and why/when are they used (to handle what types of distribution problems)?

Like the title states, I'm interested in learning about the more popular data transformation techniques. I know the internet is abound in this information, but I'd like to hear from those working ...
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### Equivalent of a flipped lognormal distribution

What distribution could represent a "flipped" (skewed left) lognormal distribution? For ex: what name would you do to the distribution in the figure below? I fitted the histogram with a Beta ...
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### Multivariate log-normal probabiltiy density function (PDF)

The Multivariate Gaussian pdf is given by $$(2\pi)^{-\frac{K}{2}} \det(\Sigma)^{-\frac{1}{2}} \exp({-\frac{1}{2}}(X-\mu)' \Sigma^{-1} (X-\mu))$$ The wikipedia for multivariate Gaussians is here ...
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### skewness and hypothesis testing (t-test and anova)

Some of my variables are heavily positive skewed (left skewed). With log transformation, some are closer to normal distribution, but some are still positively skewed, though not that bad before log ...
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### Bias of moment estimator of lognormal distribution

I am doing some numerical experiment that consists in sampling a lognormal distribution $X\sim\mathcal{LN}(\mu, \sigma)$, and trying to estimate the moments $\mathbb{E}[X^n]$ by two methods: Looking ...
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### Approximate Order Statistics for lognormal variables

Are there any known formulas that approximate the expected value of the maximum of $N$ i.i.d. lognormal random variables? I am looking for something similar to: Approximate order statistics for ...
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### Expectation of two identical lognormal distributions

I would like to compute the conditional expectation (on an interval from $c$ to $\infty$) of the minimum of two log normal distributions. Denote $X_1$, $X_2 \sim LN(0, \sigma)$, the associated ...