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Questions tagged [lognormal]

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

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If $X\sim \operatorname{lognormal}$ then $Y:=(X-d\mid x\geq d)$ has approximately a Generalized Pareto distribution

Let $X$ be a random variable with lognormal distribution. Show that when sufficiently large then $Y:=(X-d\mid x\geq d)$ is approximately a random variable with generalized Pareto distribution. Hint: ...
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Bayesian A/B test for LogNormal data

I'm currently working on a (manual) calculation for a bayesian A/B test on logNormal data. I'm currently working with simulated data to increase my understanding. It's giving me some problems, so I ...
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Interpretation of a log-level regression in its associated 'level' form

Is it conventional to interpret a least-squares regression with a log-transformed dependent variable (log-linear model) in its "level" form? In other words, running a model with the outcome in 'log ...
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Showing the expectation of a lognormal AR(1) process

Suppose I have a lognormal AR(1) process: $$\log(y_{t+1}) = (1-\theta)c + \theta \log (y_t) + \varepsilon_{t+1},$$ $$\varepsilon \sim N(0,\sigma^2)$$ To show $\operatorname{E}(y_{t+1})$, is it ...
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When is the log-normal distribution appropriate?

Iv'e read the Wikipedia entry about the log-normal distribution, as well as a few other sources online, and still do not understand what sort of natural processes are expected to produce a log-normal ...
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Sample mean lognormal variables

Suppose you've got $x_1, ..., x_n$ independant realisation drawn from a $LogNormal(\mu, \sigma^2)$. Could someone explain me why $exp(\mu + 0.5*\sigma^2)$ $\neq$ $\frac{1}{n}(x_1 + ... + x_n)$ ? Here ...
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Back transforming the intercept of double log normal distribution

I apologise if this is a duplicate, i couldn't find a thread that seem to be talking about the same thing. I have a dataset with a bunch of duration of varying lengths in seconds, i log-transformed ...
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Likelihood ratio test of log normal distribution

$X_{1},X_{2}, … , X_{n}$ be a random sample from a $𝑁(\theta, 1)$ distribution. Instead of observing $X_{1},X_{2}, … , X_{n}$, $Y_{1},Y_{2}, … , Y_{n}$ was observed where $Y_{𝑖}= 𝑒^{X_{i}}$. Find ...
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Am I Log Normalizing correctly?

I am sorry if this is a stupid question, but I have searched the other questions about log normalization found other sources on it all of which assume a level of understanding that I don't have. I ...
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Mean and error bounds of log-transformed data using Gaussian process regression

To revive a past question and establish a definitive answer, how should the mean/mode and error intervals of log-transformed data be handled when applying Gaussian process regression? For example, I ...
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Distribution of transformed multivariate log-normal

Let $\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \Sigma)$ and $\mathbf{Y} = \text{exp}(\mathbf{X})$. If $Y_i$ is one of the components of $\mathbf{Y}$, what is the distribution of $\frac{\mathbf{Y}}{...
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Conditional Expectation of Log-Normal Distribution

I want to evaluate a conditional expectation of log-normal distribution. Let $y$ be a log-normal distributed random variable. So $\log(y)\sim N(\mu,\sigma^2)$. I want to calculate $E[y-1|y-1>0].$ ...
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Log transform with 'zero' values [duplicate]

I am doing some explorative work on two large datasets. One from 2001 and one from 2018. The dataset consists of measured soil-parameters and it contains lots of zero's. From the transformations ...
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How to find the probability curve for maximum/lowest values of a random distribution?

I had asked this question on another forum but they recommended me posting here. This is my problem: I have a continuous variable where I can only measure some points of data and I need to assess the ...
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Prediction interval of Y given AR model for log(Y) [duplicate]

I have been given an AR model with seasonal variation. \begin{equation} (1-\theta_1B)(1-\theta_2B^8)(log(Y_t)-\mu)=\epsilon_t \end{equation} Setting $X_t=log(Y_t)-\mu$ one gets the following \begin{...
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Emergence of Lognormal distribution for the concentration of chemical compounds

I'm currently reviewing the literature about lognormal distributions describing/approximating the variability of a given chemical compound across different cells/ samples etc etc. The main argument ...
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Probability density function units of the log-normal distribution

In a discussion on this forum lognormal distribution, standard-deviation and (physical) units the cumulative distribution function (PDF) of the lognormal distribution was analysed. The conclusion ...
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plnorm and log scale parameters

I have expenditure data in several regions, and for each of them i know mean expenditure, standard deviation and skewness in original scale. Since data are skewed i want to compute probability of ...
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good terminology for the parameters of a lognormal distribution?

Is there any good short terminology for the two parameters of a lognormal distribution? I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
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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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What is the best point forecast for lognormally distributed data?

I believe that the values I am forecasting are lognormally distributed with log-mean $\mu$ and log-variance $\sigma^2$. I need a point forecast (i.e., a one-number summary) that minimizes the expected ...
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CDF at n of normal distribution to the nth power

I'm working with an equation that includes a normally distributed investment return R. I can find the Cumulative Distribution Function of R for the first period n=0. However, how do I derive the CDF ...
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Tests of normality - qq and Shapiro-Wilk

I am new to the world of stats... My data had a log normal distribution, so transformed by log to get it nearer normal distribution. This is real-world data. From here I want to establish if my data ...
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What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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What is the PDF for a log-log-normal distribution?

A log-log-normal distribution is a continuous probability distribution of a random variable whose logarithm logarithm $\ln(\ln(x))$ is normally distributed. What is the Probability Density Function ...
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How to generate samples of Poisson-Lognormal distribution

I would like to compute samples of the number of product purchased in a supermarket. I want to model it with a mixed Poisson lognormal distribution. Items purchased $x$ of a given consumer follow a ...
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Log-normalization of predictors

I have the following dependent and independent variables for my linear regression model. Since they are all in different scales (some of the are % others continuous variables), I was suggested to take ...
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Sum of multivariate lognormals

Is it possible to approximate the sum of multivariate lognormals using Wilkinson approximation? Any reference?
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Log Transformation in R

I need to transform my not normal distributed data to normal distributed variables. Therefore I need to log-transform them. Log10(x+1) has not worked to create a normal distribution. Therefore, I want ...
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Is “geometric mean” the same as “the first moment of the lognormal distribution”?

I would like to compare the results of two studies, one reporting "geometric mean diameter" and the other one reporting "the first moment of the lognormal size distribution". I am not sure whether the ...
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Scaling percentiles of log-normal distribution

I need help with this basic question. A study found that a variable is log-normal, with mean A and percentiles p1, p2 and p3 (could be 10%, 50% and 90%). Another study for a different group found ...
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Lognormal Distribution Probability

I'm dealing with this question, and i didn't understand should i use the $f(x)$ formula for lognormal distribution or can i calculate it with $z(P)$? Thank you for help. And i've found probability $1....
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How do I interpret the p-value from a Shapiro-Francia Test?

I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use ...
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Understanding the shifted log-normal distribution

I have difficulties understanding why a third parameter (the shift) is necessary to describe the log-normal distribution. Let's say we have a normal random variable X, if I shift this variable by an ...
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Median versus Harmonic Mean As Log Normal Data Summary

I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single ...
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Log transformation to generate random number producing NA's

I am trying to generate a random values using log distribution. The reason for using log-distribution is keep the values positive. ...
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Log-normal returns

Let $P_t$ denote a stock price distributed as $\operatorname{lognormal}(\mu , \sigma^2 )$. Suppose we construct simple returns $R_t=\frac{P_t-P_{t-1}}{P_{t-1}}$. My question is: What is the ...
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Approximating the first moment of $h(x)$ where $x$ ~${\rm log\,normal}(\mu, \sigma)$

What is the best way to approximate $E(h(X))$, where $X$ ~ Lognomal($\mu, \sigma$)? So far, I can think of Monte Carlo Methods and Gaussian Hermite quadrature as below: \begin{align} E(h(X)) &= ...
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Application of Skewness and Kurtosis

Often in finance, stock prices are considered to follow a lognormal distribution while stock returns are considered to follow a normal distribution -prices are positive while returns can be negative(...
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Statistical analysis on confidence intervals

I have a data set where the data, when plotted, is not normal. Log-transforming the data makes it normal. Should confidence intervals for the population mean and hypotheses testing about the ...
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1answer
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Sampling Methods/Monte Carlo method and Log-normal distribution

I found a problem from some notes i found online, here is a screenshot: I am trying to understand this question, it seems this function they define as the LIP() function is basically the quartile/...
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Fitting data to a log-normal distribution [duplicate]

For a simulation study I've been trying to find an appropriate distribution for job handling times in R. I have a very large dataset of 77010 records (handling time in seconds). I've been exploring ...
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Coefficient of variation (CV) of log-transformed data

I understand that with log-transformed data, the coefficient of variation (CV) on the original scale is equal to sqrt(exp(sigma^2)-1), where sigma is the standard ...
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Statistics of Extremes: Fitting the GEV distribution with MLE vs L-moments

I created a synthetic series that is supposed to simulate a series of peak discharges in blocks of years in arid catchments. The magnitudes were simulated via the Lnorm dist.: ...
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How to find the area undernearth a log-normal curve

I wanted to find the area underneath a Gaussian distribution. I found online that for an equation of the form: $Ne^{-\frac{(x-\mu)^2}{2\sigma^2}}$ The area under the curve is given by: $N \sigma \...
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Break down values in dataset to match mean and variance of another dataset

Vector A contains m variables that are log-normal distributed with mean $\mu_A$ and standard deviation $\sigma_A$. Vector B contains n variables that are log-normal distributed with mean $\mu_B$ and ...
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Hellinger distance for two shifted log-normal distributions

If I am not mistaken, Hellinger distance between P and Q is generally given by: $$ H^2(P, Q) = \frac12 \int \left( \sqrt{dP} - \sqrt{dQ} \right)^2 .$$ If P and Q, however, are two differently ...
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From log-normal parameters, to normal parameters

from the following log-normal fitting function (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html), I get the parameters [s, loc and scale]. How can I use them to get the μ ...
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Is this notation for a lognormally distributed variable misleading?

I have gotten into the habit of notating a lognormally distributed random variable $X$ as: $$X \sim \ln\mathcal{N}(\mu,\sigma^2)$$ I am now starting to question where I picked this habit up and ...
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Difference between log normal probability density values

just reviewing two resources, I noticed a difference between the log normal p.d values : One is here which takes the e to the power in which it contains ln(x) the other is here Which on page 5 , ...