# Questions tagged [lognormal]

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

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15k views

### Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.) Last year I was told that the gamma distribution is ...
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### Linear model with log-transformed response vs. generalized linear model with log link

In this paper titled "CHOOSING AMONG GENERALIZED LINEAR MODELS APPLIED TO MEDICAL DATA" the authors write: In a generalized linear model, the mean is transformed, by the link function, instead of ...
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### Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and ...
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### Whether distributions with the same moments are identical

Following are similar to but different from previous posts here and here Given two distributions which admit moments of all orders, if all the moments of two distributions are the same, then are they ...
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### How to find normal and lognormal moments, given partial information?

$Y=\ln(X)$. $X$ is lognormal and $Y$ is normal. If all I know is the arithmetic mean of $Y$ and the standard deviation of $X$. What is the formula to calculate the arithmetic mean of $X$ and the ...
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### How do I calculate a confidence interval for the mean of a log-normal data set?

I've heard/seen in several places that you can transform the data set into something that is normal-distributed by taking the logarithm of each sample, calculate the confidence interval for the ...
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### Expected value and variance of log(a)

I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
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### Priors for log-normal models

I am trying to determine what the most appropriate non-informative priors are for the two parameters of a log-normal distribution (for an accelerated failure time model). I had been working with a ...
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### Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
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### Covariance between a normally distributed variable and its exponent

Given $X \sim \mathcal{N}(\mu,\,\sigma^{2})$, what is the covariance between $X$ and $e^X$?
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### Is the product of multivariate lognormal distributions is multivariate lognormal distribution

A. Mulitivariate normal distribution case with latent variable $X$ Mapping from the low-dimensional space $X$ in Q-dimensional space (Q=2) to the high-dimensional space of $Y$ in D-dimensional space (...
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### How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
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### Multiplicative error and additive error for generalized linear model

If the following generalized linear model was used, how should I interpret the error term? link function: natural log distribution: Gamma distribution i.e., $\ln E(Y)=X\beta$ and $E(Y)=\exp(X\beta)$ ...
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### How can I convert a lognormal distribution into a normal distribution?

I have a sample of data that follows a lognormal distribution. I would like to represent the distribution as a "Gaussian" histogram and overlayed fit (along a logarithmic x-axis) instead of a ...
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### Moment Generating Function for Lognormal Random Variable

I'm working through the proof of a lognormal random variable and am having some difficulty in moving through it. I understand the following: Our CDF is $\Phi(\frac{logx - \mu}{\sigma})$, and thus our ...
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### Calculate variance and standard deviation for Log Normal Distribution

I am trying to calculate the variance and standard deviation for a log normal distribution. I was able to calculate the mean after reading this stack exchange article How to calculate a mean and ...
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### Parameters’ uncertainty for small sample size

Suppose we have a small set of numbers (5 to 10 observations), and we’re trying to fit a distribution to this set. Also, we know that all numbers are positive. I tried to fit lognormal, but I’m not ...
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### Why stock prices are lognormal but stock returns are normal

Except for the fact that returns can be negative while prices must be positive, is there any other reason behind modelling stock prices as a log normal distribution but modelling stock returns as a ...
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### How to check if my data fits log normal distribution?

I'd like to check in R if my data fits log-normal or Pareto distributions. How could I do that? Perhaps ks.test could help me do ...
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### When is it OK to write “we assumed a normal distribution” of an empirical measurement?

It is ingrained in the teaching of applied disciplines, such as medicine, that measurements of bio-medical quantities in the population follow a normal "bell curve." A Google search of the the string "...
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### Why is ln[E(x)] > E[ln(x)]?

We're dealing with the lognormal distribution in a finance course and my textbook just states that this is true, which I find sort of frustrating as my maths background isn't very strong but I want ...
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### When to use sample median as an estimator for the median of a lognormal distribution?

I myself would always use geometric mean to estimate a lognormal median. However, in the industry world, sometimes using the sample median gives better results. The question thus is, is there a cutoff ...
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### The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: \$...
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### Can quantiles be calculated for lognormal distributions?

I just talked to someone who stated that quantiles cannot be computed for lognormal distributions. or it does not make sense. Is this true?