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Questions tagged [lognormal-distribution]

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

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Comparing Gaussian GLMM models for positive, slightly non-normal data: Interpreting conflicting model selection criteria

I'm analyzing data using glmmTMB in R with the following model structure: ...
Julius Bogomolovas's user avatar
5 votes
1 answer
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In a sum of high-variance lognormals, what fraction comes from the first term?

If $X_i \overset{\textrm{iid}}{\sim} \text{Lognormal}(0, \sigma^2)$ for $i=1,\ldots,n$ and $Y_1 = X_1 / \sum_{j=1}^n X_j$, then I would expect that a particular* limiting distribution of $Y_1$, ...
Řídící's user avatar
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Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution. I think a fairly intuitive way for a lay person to ...
michaelmcandrew's user avatar
6 votes
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Delta method vs actual expectation

If $x \sim N(\mu,\sigma^2)$, then by first principles, $$\mathbb{E}(e^x) = e^{\mu + \sigma^2 / 2}.$$ I am trying to figure out where the "Delta method" is wrong here: If $(x-\mu) \sim N(0,\...
dayum's user avatar
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Autocorrelation of the lognormal Black-Scholes process

The Black-Scholes model with constant volatility $\sigma$ and interest rate $r$ is defined as $$ dS_t/S_t=rdt+\sigma dW_t $$ I derived the autocorrelation of the spot process $S_t$ for future times $0&...
Andras Vanyolos's user avatar
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Transformed Ornstein Uhlenbeck process

Say I have 𝑋 that follows an Ornstein-Uhlenbeck process: $𝑑𝑋_𝑑=πœ™X_t𝑑𝑑+πœŽπ‘‘π‘Š_𝑑$ Let $π‘Œ_𝑑=exp(𝑋_𝑑)$. How can I calculate the autocorrelation function of $Y_t$?
Isi's user avatar
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How do you determine an appropriate block length for calculating "block maxima" for GEV distribution?

I have some time series data spanning 30+ years and I am trying to do some extreme value analysis. Major disclaimer: I am not a statistician so I feel that I am wading into waters beyond my area of ...
Darcy's user avatar
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6 votes
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When to calculate the bias corrected geometric mean

Most sources give a simple equation to compute the geometric mean (GeoMean) of data samples from a lognormal distribution. GeoMean = exp(m) where m is the mean of ...
Harvey Motulsky's user avatar
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Interpreting AFT Model Coefficients: Mean vs. Median Survival Time in Log-Normal Distribution

When interpreting the coefficients of an Accelerated Failure Time (AFT) model that assumes a log-normal distribution, should we focus on the impact of coefficients on the mean survival time or the ...
ebrahimi's user avatar
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compare means of lognormal distribution

I have a small set of data that I used to generated a lognormal distribution: ...
efz's user avatar
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Using simulations to prove E[Y] formula of a log normal distribution [duplicate]

Assume that $X∼ N (ΞΌ, Οƒ^2)$ and that $Y = e^X$ and we have set $ΞΌ = 0$ and $Οƒ = 1.5$. We have to prove that $E[Y] = e^{(ΞΌ+Οƒ^2)/2}$ using 10000 simulations. I.e. ...
Markus J's user avatar
2 votes
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Is it possible to fit a linear model of y in log scale but with offset in the original scale?

Let's start with simple linear regression with log transformation of the response variable y: $$ \log(y_i) = \beta_0 + \beta_1x_i + e_i$$ (btw, how is this model called? log-linear regression or ...
Sofie's user avatar
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Expected value of the square root of a lognormal variable

Let $X$ be a positive, lognormal random variable with known mean $\mu_X$ and variance $\sigma_X^2$. Since $X$ is a lognormal random variable, I know its pdf and moment-generating function (mgf). pdf: $...
LJ Beinhauer's user avatar
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Numerical moments of a multivariate Poisson Log-normal posterior

I have a log-density of the form: $$P(\mathbf{x}) \propto \exp\left( - \mathbf{b}^{\top} e^{ \mathbf{x} } - \frac{1}{2}\mathbf{x}^{\top}A\mathbf{x} \right)$$ where $A$ is a symmetric positive definite ...
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Suppose I am using KM curve to estimate S(t) parametrically (say assuming it follows lognormal)

Suppose I am using KM curve to estimate S(t) parametrically (say assuming it follows lognormal). Now this t is in (say) months, and I want to get estimates of the lognormal curve where t is in weeks, ...
Euclidean_Space's user avatar
2 votes
1 answer
60 views

Is it ok to use the log-normal approximation for incidence rates?

I have a dataset with counts of events, population and time, and need to perform a meta-analysis of incidence rates (IRs) per person-month. By assuming random effects (thus, allowing for heterogeneity ...
Federico Tedeschi's user avatar
3 votes
1 answer
138 views

Natural log of ratios and two-way fixed-effects model bias

Bartlett and Partnoy (BP) (2020) show that OLS with natural log dependent variables that are ratios must include the $\ln(denominator)$ on the RHS in order to avoid bias (see pages 24-28) unless one ...
dcoy's user avatar
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4 votes
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Discrepancy Between Theoretical and Empirical Coefficient of Variation in Log-Normal Distribution

I'm exploring the properties of log-normal distributions and came across a formula (e.g., here) stating that the coefficient of variation (CV) of a variable $X$ following a log-normal distribution is $...
Akira Murakami's user avatar
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link log and identity in GLMER

Say that we have a GLM model with the following formula: outcome = b1x1 + b2x2 + b0 and outcome is cost, x1, x2 are independent variables Fitted using log link with gaussian distribution, so log ...
user401679's user avatar
4 votes
3 answers
467 views

Generate multivariate distributions of lognormal and normal distribution in python

I need to generate random numbers from 3 correlated distributions. First two of them are lognormal and the final one is normal, i.e. for X, ...
Xu Shan's user avatar
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How to: power analysis with log-normal distributed data

Assuming the following data: ...
ThePresident's user avatar
1 vote
1 answer
124 views

Log transformed independent variable affects other independent variables

I transformed one of my independent variables into natural logarithm form in a fixed effect panel data. This is because the data of this independent variable (i.e., EXT) is heavily skewed. This is the ...
Ahmad MHN's user avatar
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Likelihood of sum of log-normal and normal distribution [closed]

Given $y(x_t)=e^{f(x_t)}-\varepsilon _t$ with $\varepsilon _t\sim N(0,4e^{f(x_t)})$ and $f\sim GP(\mu,\sum)$. What is the likelihood $p(y|f)$? Is it $p(y|f)\sim N(e^{f(x_t)},4e^{f(x_t)})$? Thanks a ...
manhtr76's user avatar
11 votes
5 answers
333 views

When summarizing data from a lognormal distribution, when does it make sense to report the arithmetic mean vs. geometric mean

When data are sampled from a lognormal distribution with a reasonably large geometric standard deviation, the distribution is asymmetrical and the arithmetic mean will be distinct from (and larger ...
Harvey Motulsky's user avatar
1 vote
0 answers
35 views

How to convert Standarized Mean Difference to OR in skewed data?

There are many methods to convert Standarized Mean Differences to Odds Ratios for meta-analysis (ln(OR) = -1.8 SMD), but none that i have found really deals with skewed summary data. Do you think i ...
san festein's user avatar
4 votes
1 answer
105 views

Inferring distribution over concurrent events given arrival and duration distributions

Suppose you're working on infrastructure for web service and you're tasked with determining the probability distribution of concurrent requests to your services. In example, suppose the first request ...
jbuddy_13's user avatar
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Credible interval for a quantile from log-normally distributed data

Both reviewers of my latest article suggested better to work with credible intervals instead confidence intervals. Unfortunately, I am not familiar with Bayesian statistics. Until today, I was (...
chenge's user avatar
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Calculating the mean and sd of a lognormal distribution from the log mean and log 5th percentile [duplicate]

I have a mean and 5th percentile value from river flow data that are assumed to follow a log-normal distribution. From these, I need to calculate the the mean and SD of the underlying normal ...
Pau's user avatar
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3 votes
1 answer
492 views

Lognormal including 0

I'm trying to model a random variable $X_i$ related to updates in prices. The updates in prices are always non-negative, and my random variable is the update coefficient. For example, if product $a$ ...
Santiago's user avatar
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Should I back-transform estimate and 95%CI after a survival analysis with log-normal distribution?

I need to run a survival analysis on my data. Based on the AIC, the lognormal distribution is the most suited one. Can I report the estimates and 95% CI as they are, or do they need back-...
MWE_Manet's user avatar
1 vote
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Develop a model for theoretical best performances at different ultra running distances/times

Goal Develop a model for theoretical best performance for running distances from marathon to around 1000 km. Partly to compare the strength of ultrarunning world records, but more importantly, to get ...
Daniel Westergren's user avatar
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78 views

Fitting truncated sample to normal distribution with unknown mean & variance

I have data that is somehow truncated. It is a list of log best performances from events, where different events have different cutoff times. How could it be possible to find the unknown mean and ...
Daniel Westergren's user avatar
2 votes
1 answer
152 views

How to derive a random variable's standard error and mean with its log-normal distribution estimation

I am trying to do a meta-analysis, but I met some papers which estimate the key parameter (i.e., $\alpha$) by assuming its log follows a normal distribution (i.e., $\ln(\alpha)$ ~ $N(\mu, \sigma^2)$). ...
Wu Jilong's user avatar
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388 views

Deriving 99th percentile in log-normal data using transformed normal distribution?

My aim is to calculate the 99th percentile of the log-normally distributed data on the left-hand side. There are various approaches described to do this, e.g. ranking data and then selecting the value ...
wptmdoorn's user avatar
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0 answers
15 views

Mixed-effects model when the response has two distinct distributions for two levels of an explanatory factor

I have a continuous response variable called "distance," which was measured in two different years (2019, 2020), and each year exhibited a significantly different distribution. In 2019, the ...
user7618183's user avatar
0 votes
2 answers
128 views

Why is the log of the mean of a draw from rlnorm different than the meanlog used to generate it?

I'm trying to verify that I'm using rlnorm correctly. I made the following script ...
W Floyd's user avatar
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0 answers
30 views

Expectations with respect to affine transformation of a log-normal distribution

Let $X$ be a log-normal distribution and consider $Y=aX+b$ for some $a,b>0$. I would like to know if one can compute $$\mathbb{E}[\log(Y)]$$ This would be very easy if it was $b=0$, since in this ...
Francesco Bilotta's user avatar
0 votes
1 answer
44 views

Log-normal ratio implies numerator/denominator are log-normal

Let $X$ and $Y$ be two positive random variables defined over $(\Omega,\mathscr{F},\mathbb{P})$. We know that if they are both log-normal then the random variable $Z$ defined as: $$Z:=\ln\frac{X}{Y}$$ ...
Daneel Olivaw's user avatar
1 vote
2 answers
175 views

Calculate mean of density function (example using lognormal distribution)

In a lognormal distribution, the mean is equal to $\exp(\mu + \frac{\sigma^2}{2})$. I tried to separately calculate this using the definition $E[X] = \int{xf(x)dx}$, where I have 200 $x$ values evenly ...
a11's user avatar
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Truncated lognormal distribution calibration with MME

To estimate the parameters of a truncated distribution (lognormal for example), we can use the Maximum Likelihood Estimation or Method of Moments. For the Method of Moments Estimation, one needs to ...
John Smith's user avatar
3 votes
2 answers
128 views

Convolution of two functions doesn't fit my data as I thought it would

I have simulated a Gaussian curve in 50 bins of data. I have then repeated this many times, drawing the amplitude of the Gaussian from a log-normal distribution. Here are a 10 realizations: (IMAGE 1) ...
user1551817's user avatar
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3 votes
3 answers
110 views

Computationally feasible way to fit data generated by sum of log normal and normal variables

I often run into data that has effects that go across a wide range of scales and are roughly log-normal, yet also have normal error terms added in, occasionally making some terms negative. Is there ...
Mark Miller's user avatar
1 vote
1 answer
38 views

Is this the correct approach for fitting a lognormal distribution with known population mean to given data?

I have some incomplete data for loss ratios (=loss/revenue) for 5 years. Let's call it X. Suppose these are the given values for X: 2012 - 73%; 2013 - 67%; 2014 - 78%; 2015 - 81%; 2016 - 75%; I was ...
LilStats's user avatar
3 votes
1 answer
64 views

Does this approach to simulation for survival analysis, of breaking the analysis into deaths versus survivors, appear reasonable?

I've spent last several weeks learning about survival analysis, see one of the last posts at How to simulate variability (errors) in fitting a gamma model to survival data by using a generalized ...
Village.Idyot's user avatar
2 votes
1 answer
85 views

How to generate random values representing lognormal parameters for simulating the lognormal distribution using survival data in R?

I am trying to generate random parameters for the lognormal distribution in order to test parameter sensitivity and for simulating (predicting) future survival rates, using the ...
Village.Idyot's user avatar
0 votes
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36 views

Gaussian Log Probability [duplicate]

I have a code segment from this repo: https://github.com/toshikwa/slac.pytorch/blob/master/slac/utils.py I am reading a paper about Soft Actor-Critic, a reinforcement learning algorithm. They have ...
chadmc's user avatar
  • 1
3 votes
1 answer
412 views

How to extract the correct parameters for the lognormal distribution when using the survreg() function in survival analysis?

I am testing simulation of the lognormal distribution against the lung dataset, as an example of right-censored data, from the ...
Village.Idyot's user avatar
0 votes
1 answer
39 views

How do sample size and measurement accuracy affect the measurement of the parameters of a log-normal distribution?

Assume that we have objects (e.g. particles) whose properties (e.g. diameter) follow a log-normal distribution that can be described by a geometric mean $\mu_g$ and a geometric standard deviation $\...
Nos's user avatar
  • 315
1 vote
1 answer
105 views

Difficulties finding location and scale parameters from PDF [duplicate]

I am having difficulty finding the correct location and scale parameters for a PDF diagram that I need to validate my data. I have already calculated the location parameter to be -1.01, but I am ...
Agis Fitrony's user avatar
2 votes
2 answers
157 views

Log-normal model of data with unknown offset

I have a bunch of samples that, empirically speaking, appear to be drawn from an unknown log-normal distribution, with an unknown constant offset applied to the data points. That is, $\ln(X_{i} + C) \...
TLW's user avatar
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