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

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How to test whether part of the sample follows log-normal distribution?

I have a sample data that look like the following figure in a Q-Q plot with log-normal distribution. I performed an Shapiro normality test on the logarithm of the data, and reject the null hypothesis ...
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56 views

Weighting observations and measurement uncertainty in bayes

I am working on using MCMC (via STAN) to estimate model parameters for a bunch of observations with measurement uncertainty. I'm having problems with weighting each observation, and have reduced the ...
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8 views

How to reconstruct moments from aggregated data?

Let $X_{1\ldots n}$ be a stochastic variable that is log-normal distributed, with parameters $\mu$ and $\sigma$. Now suppose all $X_i$ are aggregated into $Y_{1\ldots m}$ where $Y_1$ is the mean of ...
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110 views

Can quantiles be calculated for lognormal distributions?

I just talked to someone who stated that quantiles cannot be computed for lognormal distributions. or it does not make sense. Is this true?
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45 views

Simulating lognormal data - not just log(mean) and log(sd)?

According to this question, to simulate a log-normal dataset with a mean and SD known, you just enter log(mean) and log(sd). For example, lets say I wanted a mean of 5 and SD of 2. ...
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122 views

Confidence Interval of a Lognormal Random Variable

Just learning some stats, so please forgive if this is simple but I couldn't find a good explanation. Let $X \sim \mathcal{N}(\mu,\sigma^2)$ and $Y = e^X$. To find an approximately 95% confidence ...
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30 views

Lognormal distribution using normal distribution inputs

I'm simulating lognormal data in R log(Y), using the mean and standard deviation of Y. This article outlines it very well! One step in the article I'm having trouble solving how it works though. ...
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35 views

How to calculate log-normal distribution parameters with partial data?

Imagine we have a partial data and we know that this partial data represent only the left 5% of the log-normal distribution, which the overall data follow. How can we calculate the mean-log and sd-log ...
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116 views

Lognormal Regression?

I'm trying to model a lognormal response variable. I want to take the log of the response variable and do a least-squares regression line over my predictive variable. However, I'm worried about ...
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14 views

estimating a survival function using a lognormal distribution

I am trying to fit multiple distributions to survival data. Now I am having some trouble with the lognormal distribution. I want to use the following formula: S(t)=1-Φ((log t-mu)/ σ My outputs from R ...
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59 views

fitting parametric survival curves on Kaplan Meier probabilities in aggregate data

Lets suppose I have aggregate survival probabilities (NOT individual level data) from Kaplan Meier curves. I would like to curve fit different "types" of distribution like exponential, weibull, ...
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63 views

Why are server response times distributed lognormally?

I found out that webserver response times are typically modeled as coming from a lognormal distribution here. What I don't quite get is why this is the case! In particular, Wikipedia states that a ...
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34 views

Correlation / clustering over lognormal data

I'm working with some financial data and it turns out my data is pretty much lognormal distributed. The question I have is, which produces "better" results: using plain data to find correlation / ...
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786 views

How to avoid log(0) term in regression

I have following simple X and Y vectors: > X [1] 1.000 0.063 0.031 0.012 0.005 0.000 > Y [1] 1.000 1.000 1.000 0.961 0.884 0.000 > > plot(X,Y) I ...
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Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and ...
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51 views

Can I make a linear congruential generator with a lognormal distribution?

One of my class tasks is to make a simulation. I've gathered the data and done distribution fitting to it and the result of the distribution is log-normal. I have the code to generate random numbers ...
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23 views

Name for phenomenon which causes bias in estimation of extreme percentiles of a distribution fitted to points with large error bars

I have a series of small numbers (say 25-45) of values which were generated, and each value has an uncertainty associated with it. I also have a theory that says these points are supposed to fit well ...
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31 views

Correction for Log normal distribution

Context: I have observed continuous data $\boldsymbol{O}$, for each observation $i$ I have an assumed known $\sigma_i$ for each observation I have an expected model value $E_i$. $E_i$ was produced ...
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85 views

How to derive the cdf of a lognormal distribution from its pdf

I'm trying to understand how to derive the cumulative distribution function for a lognormal distribution from its probability density function. I know that the pdf is: $$f(x) ...
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72 views

How to fit discrete data that have mode 0 to a log-normal distribution?

I am trying to figure out how to fit a log-normal distribution to discrete data that have mode 0, in particular, without first removing the zeros. For example, paper citation data are said to be ...
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1answer
62 views

Hypothesis testing- lognormal distribution

I have a conditional mean and standard error for a parameter log-normally distributed. I want to test whether the mean of the distribution is significantly different from an alternate estimate of ...
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20 views

The distribution of a product between a Lognormal and a Beta is …?

I have to random variables expressed as $1 \times 1000$ vectors. One of the vectors $B$ is Beta distributed while the other $L$ is lognormal distributed. Upon element-wise multiplication, I get vector ...
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43 views

Estimating the variance of a sum of predictions

I have $N$ plots that were used to estimate a relationship between three predictor variables, $X_1$, $X_2$, $X_3$, and an outcome, $Y$, using a generalized linear (lognormal) model. The resulting ...
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Find the mean of lognormal rv's with available variance and the sum of rv's

I have the sum of a bunch of random variables $S$, v = [1 1 2 2 3 3 4 ...]; S = sum(v); I know that vector $v$ is lognormally distributed, BUT I DON'T KNOW IT. ...
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70 views

How to describe a function of two normal distributed random variables

I consider the generic problem $W(X,Y)=-2\ln(\frac{(X-Y)^2}{2(X^2+Y^2)})$ where $X$ and $Y$ are normally distributed random variables Can I make any statements about the distribution of $W$?
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39 views

Regression against polynomials and log-linear predictors

I have a regression problem where one of the predictors has a very good fit as $Y \sim poly(X_1, 2)$. However, $Y$ is clearly log-linear against my second predictor $X_2$, so $ln(Y) \sim ln(X_2)$. ...
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148 views

How to estimate parameters of a log-normal distribution?

I am using income data from the Current Population Survey for a small undergrad economics paper. In economics, there is evidence that the income of 97%–99% of the population is distributed ...
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26 views

Gamma Distribution with Percentages

I am dealing with a set of data that appears to follow a gamma distribution or a lognormal distribution but the only issue is that the data set is in percentages and both of these distributions don't ...
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200 views

Percent change interpretation in log-transformed regression: Percent change from what?

I am dealing with a regression model where both the DV and IV are log-transformed. I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in ...
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Continuous distribution for discrete population: Assessment?

We model Inflow and Outflow [people per day] by means of stochastic processes. We would like to assess to what extent the resulting continuous distributions acceptably model the discrete variables. ...
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41 views

Forming Location-Scale Family for Log-Normal

For the random variable X with a log-normal pdf $f(x)=\frac{1}{\sqrt{2*\pi}}x^{-1}e^{-.5*log(x)^2}$ I am trying to find a location-scale family $h(x)$ such that $h(x)$ has mean 0 and variance 1 Now ...
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57 views

Distribution of proportions relative to sum of random variables

Let $X_1,...,X_n$ be iid lognormally distributed variables and $X_{sum} = X_1+...+X_n$. What is the distribution of $\frac{X_k}{X_{sum}}$ for each $k$ in $1..n$? What are their density functions? ...
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112 views

Mixture of Gaussians on Log of Data

I am practicing Mixture of Gaussians and found the below dataset snoq, which is the precipitation amounts recorded at a US region, with ...
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29 views

Combining two data sets with different weightings, possibly Bayesian Updating?

I am a PhD student and I am currently looking at railway track degradation. As part of this I am finding linear fits of the track geometry recordings against time to give a degradation rate. The ...
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9 views

Finding significant values in my tree-like distributed data

i have a question about my data. Let me first describe what i know about it. I know that the number of data points I have is large (200-1000) I know each data point value is greater or equal to 0 I ...
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76 views

Tests for lognormal distribution

I have some data in the following manner. 10 3 4 5 6 9 ... I have to check that the difference between returns is log normal by doing ln(return/previous return). I know some tests for normality if i ...
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46 views

Error propagation - nonnormal (again)

I have a dataset of ~2000 points. Each of those points has a standard error value associated with it, and it is assumed that the data points and errors are uncorrelated. Both the dataset and the ...
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1answer
93 views

KL divergence between a gamma distribution and a lognormal distribution?

Is there a closed-form formula for the following KL divergence? $D_{KL}(X,Y)$ where $X \sim \mathrm{Gamma}(k,\theta)$ and $Y \sim \mathrm{LogNormal}(\mu,\sigma^2)$
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Finding a distribution for data in $\mathbb{N}_0$

Suppose, we have a set of 10,000 individuals. Each individual falls into exactly one of 200 categories. [Edit: The categories are phenotypes (different potential outcomes) of the one property that is ...
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368 views

Expectation, Variance and Correlation of a bivariate Lognormal distribution

If $Y \sim N(\mu,\sigma^2)$ is normally distributed, then $X=\mathrm{e}^Y$ is lognormally distributed. To get the log-$\mu$ and log-$\sigma$ of this lognormal distribution you calculate $$\sigma^2 = ...
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43 views

Constant default probability in Merton Model

The Merton model says we have a geometric brownian motion $V(t)$ with drift $\mu$ and volatility $\sigma$. Thus $$V(t)=V(0) \exp\left(\sigma W(t)+(\mu-\frac{1}{2}\sigma^2)t\right)$$ where $W(t)$ is a ...
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3answers
119 views

Mean test of log-normal distibutions

I have two data sets, which are assumed to be log-normally distributed. How can I test whether their means are statistically different from each other? I guess I cannot use the 2-sample t-test, ...
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68 views

Remapping the Sum of two Normal Random variables?

I have a problem where I have sum of two random variables 1). Each distributed independently normally with different means ($\mu_1$, $\mu_2$) and sds ($\sigma_1$, $\sigma_2$). $Z=R_1+R_2$ 2). Each ...
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252 views

Interpreting negative binomial regression with log transformed independent variables

My independent variables were highly skewed, so to normalise the distribution they were log transformed. Also since there were zeros in the data, I've added + 1 to transform the variables. This is ...
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1answer
23 views

Picking a probability distribution for observed intensities

I have an experiment that measures "intensity" (in this case, electron density of a molecule) on a grid. The values it gives are non-negative,. I'd like to write a likelihood for this observation ...
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Problem with multivariate lognormal distribution in R

I'm using the R package compositions for the multivariate lognormal distribution. this is the only package I found that supports it. However I'm not sure how this ...
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1answer
54 views

simulating two correlated lognormal AR(1) time series

I'd like to simulate 2 correlated lognormal AR1 time series. I have already found this post which is the answer for 2 Normal AR1 time series How to simulate two correlated AR(1) time series? I've ...
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2answers
39 views

Lognormal with negative mean?

I have a set of cycle time data for a processing counter. Since the cycle time is less than 1 minute, so the time taken are all less than 1 (ie 0.14m). I am trying to fit a distribution, but result ...
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793 views

Why stock prices are lognormal but stock returns are normal

Except for the fact that returns can be -ve while prices must be +ve, is there any other reason behind modelling stock prices as a log normal distribution but modelling stock returns as a normal ...
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107 views

Use of normality test to distinguish gamma from log-normal distribution

I have random population sample data that I would like to describe using a distribution. If I plot the estimated kernel density, the data appear positively skewed and using functions in R such as ...