Questions tagged [lognormal-distribution]

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

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How are bivariate lognormal parameters related to the underlying normal parameters?

If $Y∼N(μ,σ^2)$ is normally distributed, then $X=\exp(Y)$ is lognormally distributed. The parameters for a univariate distribution, $\mu$ and $\sigma$ of this lognormal distribution are given by $$\mu{...
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Estimated lognormal PDF shifted compared to data

I have experimental data (~100k observations) that appear to be from a lognormal distribution. I am attempting to estimate the distribution parameters using ...
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Intuition for why mean of lognormal distribution depends on variance of normally distributed rv

Let $X\sim\mathcal{N}(\mu,\sigma^2)$, which is a normal distribution. Then, $\text{exp}(X)\sim\text{Lognormal}(\mu,\sigma^2)$, and its mean is $$ \mathbb{E}[\text{exp}(X)]=\text{exp}\left(\mu+\dfrac{\...
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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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MLE of log-normal distribution with one parameter

Suppose we have a sample of random variables $X_1, \cdots, X_n$ that are from a log-normal distribution, where $\log X_i \sim N(\mu,\mu^2)$ (same variance and mean). Find the MLE $\tilde{\mu_n}$ of $\...
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Is there a statistical test for the goodness of fit of an estimated lognormal distribution of Data

I am trying to test the goodness of fit of my estimated distribution for some data I have, called "dt_arrival", using Python. My Data I used the Fitter library as follows, which told me that ...
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Standard Deviations of Detrended Data vs Original Data

I'am interested to know the opinion on this matter. I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the ...
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Distribution of sum of independent but not i.i.d. lognormal variables?

I am trying to find the distribution of the following variable Z: $X_i$ are each independent with Lognormal distribution ($\mu_i, \sigma^2_i$), $X_i \in L^2$ forall $\forall i$ Z = $\sum_i cX_i$ where ...
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How to derive sales contribution in a log-log regression media mix model?

I am working on a media mix model to determine how different media channels impact sales. Since there is a non-linear relationship between sales and media spend, I needed to apply a log transformation ...
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How to test if one histogram bin has higher count than expected?

I'm studying the ratio $(A/B)$ of two physical constituents $A$ and $B$ that reside in each sample. It's hypothesized that $A$ and $B$ can "split" not unlike cells - if A duplicates before B ...
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How to construct confidence intervals for log normal using boot function in R

So, the sample mean for the log-normal is defined as $exp(\mu + \sigma^2/2)$. So, I made the boot statistic function as follows: ...
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Goodness of fit for large, weighted sample

I have several thousands samples that I want to test for lognormality. Each sample is independent, and the number of data points in a given sample varies over several orders of magnitude (100 to ~100k ...
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Difference in using mean of log(X1),log(X2)...log(Xn) vs. geometric mean (X1,X2,Xn)?

I have positively skewed data that I had to transform to log(). The observations are distributed across 3 groups. For example, in group #1: I calculated the geometric mean of the raw data (GM = 224), ...
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Unsure how to analyze count data. Plot the logarithm?

My experiment consisted in turning off multiple genes separately from each other and counting a certain type of cells (say cells A). For each gene I had around 20 organs for which I counted cells A. ...
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Describing the distribution of half-lives from highly uncertain data

I am a medical doctor working on a project within the field of pharmacokinetics. A lot of detailing is required, so please bear with me. The aim is to describe the distribution of half-lives of a drug ...
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Bland-Altman with non-normally-distributed differences and "0" values in one of the two series of measurements

I have two series of measurements of the same variable, coming from two different methods. The variable is represented by the weekly intake of a contaminant through diet. One method is a Food ...
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A statistical model of air pollution

I am currently studying a course in statistical mathemathics at for a degree in engineering. We have this project regarding a fictional scenario of air pollution. The current assignment is to answer ...
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Adding a lognormal distribution into a model of shot noise for a Poisson process to calculate moments of the process

I'm working with a simple 1D model of some objects propagating through a domain, $x$. The setup is like shot noise, and is actually taken from a paper by Militello, F., and Omotani, J. T, 2016 Nucl. ...
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What is a good symmetrical loss function for relative errors

I am interested in using the squared log-difference between predictions and observations as a loss function, it appears to me to be a very natural way of dealing with errors where these are expected ...
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What is the formula for the Mean & Variance for this Log Normally Distributed Variable

I am having trouble finding the mean and variance for this log normal distribution.
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Do stock price changes follow Pareto Distribution? [closed]

I calculated the distribution of the stock price daily ratios. The ratios are multiplicative, $d_t=p_{t} / p_{t-1}$. As far as I know the distribution should look like Power law distribution (Pareto ...
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When and how to transform data in regression tasks [duplicate]

I'm studying linear regression tasks and some transformation of data, in order to make the model linear, and to make the L-I-N-E assumption of linear regression met. I know that if we have a non-...
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Why I cannot generate random numbers having a truncated lognormal distribution?

My deduction is: When the distribution is truncated, a normalization factor should be introduced: \begin{equation} g(x) = \frac{C}{x\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{\ln{x}-\mu}{\sigma}\...
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For an log-normally distributed $X$, what is the pdf of $Y = c \cdot X^a$?

Since a few days I tried figure this out but I am stuck. Imagine there is an random variable $X$ which is distributed log-normally such that there is an normal distributed $Z \sim N(\mu,\sigma^2)$ ...
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What is the resulting function to describe a log-normal function with Gaussian noise added?

I have a log-normal distribution: $\frac{1}{x} Ae^{-\frac{(ln(x)-\mu)^2}{2\sigma^2}}$ And I draw from it (1000 times) and plot the draws in a histogram: The log-normal function from which the draws ...
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How to get mu and sigma from a population containing multiples lognormal distributions

Let's say that I have a data set that contains 3 different lognormal populations. How is the way to get each parameter (mu and sigma) from each population? I am representing the problem as follows: <...
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Mean, Median, Mode of Log Normal Distribution

Let $Y$ be Log-Normal with parameters $\mu$ and $\sigma^{2}$. So $Y=e^{x}$ with $X \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$. Which of the following statements is correct? (A) The median of $Y$ is ...
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