# Questions tagged [lognormal-distribution]

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

683 questions
Filter by
Sorted by
Tagged with
32 views

### 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: ...
205 views

### 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 $Y_1$, ...
• 195
329 views

### 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 ...
596 views

27 views

### Transformed Ornstein Uhlenbeck process

Say I have 𝑋 that follows an Ornstein-Uhlenbeck process: $𝑑𝑋_𝑡=𝜙X_t𝑑𝑡+𝜎𝑑𝑊_𝑡$ Let $𝑌_𝑡=exp(𝑋_𝑡)$. How can I calculate the autocorrelation function of $Y_t$?
• 1
1 vote
42 views

### 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 ...
• 915
154 views

### 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 ...
• 20.9k
32 views

### 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 ...
• 291
42 views

### compare means of lognormal distribution

I have a small set of data that I used to generated a lognormal distribution: ...
• 101
43 views

### Using simulations to prove E[Y] formula of a log normal distribution [duplicate]

Assume that $X∼ N (μ, σ^2)$ and that $Y = e^X$ and we have set $μ = 0$ and $σ = 1.5$. We have to prove that $E[Y] = e^{(μ+σ^2)/2}$ using 10000 simulations. I.e. ...
• 23
28 views

### 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 ...
• 21
1k views

22 views

### 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 ...
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, ...
• 163
67 views

### How to: power analysis with log-normal distributed data

Assuming the following data: ...
• 131
1 vote
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 ...
1 vote
22 views

### 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 ...
• 11
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 ...
• 20.9k
1 vote
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 ...
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 ...
• 3,394
60 views

### 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 (...
• 35
1 vote
85 views

### 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 ...
• 113
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 $a$ ...
• 133
15 views

### 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-...
1 vote
44 views

### 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 ...
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 ...
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., $\ln(\alpha)$ ~ $N(\mu, \sigma^2)$). ...
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 ...
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 ...
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 ...
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 ...
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: $$Z:=\ln\frac{X}{Y}$$ ...
1 vote
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 ...
• 133
59 views

### 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 ...
• 250
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) ...
• 1,233
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 ...
• 233
1 vote
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 ...
• 11
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 ...
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 ...
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 ...