# Questions tagged [lognormal-distribution]

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

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### Asset prices are in theory log-normally distributed

In finance, the price of an asset is given by the following formula. $P_t=P_0* e^r$ r=returns Pt = Price at time "t". P0 = Actual Price. Likewise, it is assumed that the yields (r) will ...
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### Is return normal or log normal?

I read that return is normal and stock price is log normal. But I also read that return is log normal. So I am confused about which it is. In the 14th Chapter of Options, Futures, and other ...
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### Log-normal mean and standard deviation change after sampling

I have the log-normal standard deviation and the mean that I want to use to sample from a log-normal distribution in Python. However after I do the sampling and compute the arithmetic mean and ...
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### Convert from log-normal distribution to normal distribution [duplicate]

For purposes of sampling I have the variance v and mean m of a log-normal distribution, I don't want to directly sample from the log-normal distribution so my question is how can I convert this into a ...
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### the mean and standard deviation aren't the same as those of the input data i provided after sampling

I have a log-normal mean and a standard deviation. after i converted them to the underlying normal distribution's parameters mu and sigma, I sampled from the log-normal distribution however when i ...
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### Distribution of the product of two LogNormals [duplicate]

Reading the wiki I saw the statemeent that: "The distribution of the product of two random variables which have lognormal distributions is again lognormal. This is itself a special case of a more ...
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### 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 ...
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### Bias Correction and Variance Estimation of Inverse Log-Linear Regression

My question is related to this one, but it has no answers or comments. So, I try to ask with a different way. I have a physical quantity $X > 0$ and a noisy sensor $Y$ which has the following ...
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### Transforming skewed distribution of dependent variable in linear regression?

As I understand it, the skewness of the response variable in a linear regression does not need to be normal (only the residuals need to be normally distributed). However, I was generally wondering if ...
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### How to interpret linear regression with log10 dependent variable

I have run a linear regression in R where independent variable = X and dependent variable = log10(Y). The results indicate that r2 = 0.11 and p = 0.04. Now how can I calculate the percentage of ...
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### Sample Geometric Mean and Sample Median of a Log-Normal Random Variable

The Wikipedia article for the log-normal distribution states that the geometric mean and median of a log-normal random variable are equal. However, when I simulate log normal data with a small N, ...
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### Weibull and Lognormal Fits

I have simulated failure time data for some components. I tested whether a Weibull or lognormal distribution best fit the data. Please see Figures below. The figures provide median and $95\%$ ...
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### How can you express a two lognormal distribution in two independent standard normal distributions?

Okay so if I have a equation that says the deflection of a beam is $$D = \frac{L*F}{R}$$ Where D is displacement L = length F= force R= resistance And I was told that The force and the resistance ...
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### Extracting descriptive parameters from XY curves

I recorded XY data from many individual cells responding to a stimulus (Concentration of Molecule A (Y-axis) ~ Time (X-axis)) (see image below for three such cells). How can I extract descriptive ...
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### product of log-normal variables

I'm trying to figure out some "paradox" that I don't understand. I want to model the evolution of some quantity (eg price), my assumption is that from one time step to the next, I will ...
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### Risks for the Coefficient of Variation when using very skewed (log-transformed) data

I have many datasets which I have normalized using log-transformation, however for some datasets the log-transformation did not improve the skewness that good (still close to 1). For these datasets, I ...
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### Different method of moments technique for Lognormal Distribution

We consider a random sample $X_1,...,X_n$ from a lognormal distributed random variable $X$ with density function f_X(x;\mu,\sigma)=\frac{1}{x\sigma\sqrt{2\pi}}e^{-\frac{1}{2\sigma^2}(\ln(x)-\mu)^2},\...
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### Goodness of fit of a distribution obtained by minimizing a log-loss function

I am trying to fit a log-normal distribution to a time-to-failure data of a product, but the data to which I want to fit the distribution is not regular data. In the data, every row $i$ has two pieces ...
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### Linear regression to predict both mean and SD of dependent variable

Imagine we were to investigate the relationship between people's annual income and daily food expenditure in a fictional population. The following example is not meant to be realistic, but hopefully ...
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### The product of two lognormal distributions may not be a lognormal

If two lognormal random variables $X, \:Y$ are neither independent nor jointly normally distributed, the product $XY$ may not be lognormally distributed. Where can I find the explanation for the 'may ...
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### Estimate population mean from sample with known distribution

My sample size is around 100k - should be enough for CLT to work. One intuitive approach is to estimate population mean by sample mean y. However, after plotting the sample data, I notice the ...
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### Differential entropy of a multivariate log-normal distribution

Let $Y$ be a multivariate log-normal random variable. As such, $\ln(Y)$ follows a multivariate normal distribution, which I denote by $\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\Sigma})$. I already ...
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### log-normal distribution of raw data vs. normal distribution of log data

I often assume that my data follow the normal distribution (concentrations of various pollutants in biota). The definition says that the data follow the log-normal distribution when normally ...
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### One Sample T-Test - Data Transformation

I apologize in advance is this question seems very elementary. It has been a long time since I have dabbled in significance tests and I can't seem to find an answer to this anywhere else. I have a ...
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